diff --git a/parse/train/3hGNqpI4WS/3hGNqpI4WS.md b/parse/train/3hGNqpI4WS/3hGNqpI4WS.md new file mode 100644 index 0000000000000000000000000000000000000000..c1896d7fe513f1de02336bd97d064475a3bc2243 --- /dev/null +++ b/parse/train/3hGNqpI4WS/3hGNqpI4WS.md @@ -0,0 +1,562 @@ +# DEPLOYMENT-EFFICIENT REINFORCEMENT LEARNING VIA MODEL-BASED OFFLINE OPTIMIZATION + +Tatsuya Matsushima∗ Hiroki Furuta∗ Yutaka Matsuo The University of Tokyo {matsushima, furuta, matsuo}@weblab.t.u-tokyo.ac.jp + +# Ofir Nachum + +# Shixiang Shane Gu + +Google Research + +{ofirnachum, shanegu}@google.com + +# ABSTRACT + +Most reinforcement learning (RL) algorithms assume online access to the environment, in which one may readily interleave updates to the policy with experience collection using that policy. However, in many real-world applications such as health, education, dialogue agents, and robotics, the cost or potential risk of deploying a new data-collection policy is high, to the point that it can become prohibitive to update the data-collection policy more than a few times during learning. With this view, we propose a novel concept of deployment efficiency, measuring the number of distinct data-collection policies that are used during policy learning. We observe that naïvely applying existing model-free offline RL algorithms recursively does not lead to a practical deployment-efficient and sample-efficient algorithm. We propose a novel model-based algorithm, Behavior-Regularized Model-ENsemble (BREMEN), that not only performs better than or comparably as the state-of-the-art dynamic-programming-based and concurrently-proposed model-based offline approaches on existing benchmarks, but can also effectively optimize a policy offline using 10-20 times fewer data than prior works. Furthermore, the recursive application of BREMEN achieves impressive deployment efficiency while maintaining the same or better sample efficiency, learning successful policies from scratch on simulated robotic environments with only 5-10 deployments, compared to typical values of hundreds to millions in standard RL baselines. + +# 1 INTRODUCTION + +Reinforcement learning (RL) algorithms have recently demonstrated impressive success in learning behaviors for a variety of sequential decision-making tasks (Barth-Maron et al., 2018; Hessel et al., 2018; Nachum et al., 2019). Virtually all of these demonstrations have relied on highly-frequent online access to the environment, with the RL algorithms often interleaving each update to the policy with additional experience collection of that policy acting in the environment. However, in many real-world applications of RL, such as health (Murphy et al., 2001), education (Mandel et al., 2014), dialog agents (Jaques et al., 2019), and robotics (Gu et al., 2017a; Kalashnikov et al., 2018), the deployment of a new data-collection policy may be associated with a number of costs and risks. If we can learn tasks with a small number of data collection policies, we can substantially reduce them. + +Based on this idea, we propose a novel measure of RL algorithm performance, namely deployment efficiency, which counts the number of changes in the data-collection policy during learning, as illustrated in Figure 1. This concept may be seen in contrast to sample efficiency or data efficiency (Precup et al., 2001; Degris et al., 2012; Gu et al., 2017b; Haarnoja et al., 2018; Lillicrap et al., 2016; Nachum et al., 2018), which measures the amount of environment interactions incurred during training, without regard to how many distinct policies were deployed to perform those interactions. Even when the data efficiency is high, the deployment efficiency could be low, since many on-policy and off-policy algorithms alternate data collection with each policy update (Schulman et al., 2015; Lillicrap et al., 2016; Gu et al., 2016; Haarnoja et al., 2018). Such dependence on high-frequency policy deployments is best illustrated in the recent works in offline RL (Fujimoto et al., 2019; Jaques et al., 2019; Kumar et al., 2019; Levine et al., 2020; Wu et al., 2019), where baseline off-policy algorithms exhibited poor performance when trained on a static dataset. These offline RL works, however, limit their study to a single deployment, which is enough for achieving high performance with data collected from a sub-optimal behavior policy, but often not from a random policy. In contrast to those prior works, we aim to learn successful policies from scratch in a manner that is both sample and deployment-efficient. + +![](images/d4b7db2b7c0236b75d1498e37817a81892cf444ccaaf33effb12564d6ca2dc21.jpg) +Figure 1: Deployment efficiency is defined as the number of changes in the data-collection policy $( I )$ , which is vital for managing costs and risks of new policy deployment. Online RL algorithms typically require many iterations of policy deployment and data collection, which leads to extremely low deployment efficiency. In contrast, most pure offline algorithms consider updating a policy from a fixed dataset without additional deployment and often fail to learn from a randomly initialized data-collection policy. Interestingly, most state-of-the-art off-policy algorithms are still evaluated in heavily online settings. For example, SAC (Haarnoja et al., 2018) collects one sample per policy update, amounting to 100,000 to 1 million deployments for learning standard benchmark domains. + +Many existing model-free offline RL algorithms (Levine et al., 2020) are tuned and evaluated on massive datasets (e.g., one million transitions). In order to develop an algorithm that is both sample and deployment-efficient, each iteration of the algorithm between successive deployments has to work effectively on much smaller dataset sizes. We believe model-based RL is better suited to this setting due to its higher demonstrated sample efficiency than model-free RL (Kurutach et al., 2018; Nagabandi et al., 2018). Although the combination of model-based RL and offline or limiteddeployment settings seems straight-forward, we find this naïve approach leads to poor performance. This problem can be attributed to extrapolation errors (Fujimoto et al., 2019) similar to those observed in model-free methods. Specifically, the learned policy may choose sequences of actions which lead it to regions of the state space where the dynamics model cannot predict properly, due to poor coverage of the dataset. This can lead the policy to exploit approximation errors of the dynamics model and be disastrous for learning. In model-free settings, similar data distribution shift problems are typically remedied by regularizing policy updates explicitly with a divergence from the observed data distribution (Jaques et al., 2019; Kumar et al., 2019; Wu et al., 2019), which, however, can overly limit policies’ expressivity (Sohn et al., 2020). + +In order to better approach these problems arising in limited deployment settings, we propose Behavior-Regularized Model-ENsemble (BREMEN), which learns an ensemble of dynamics models in conjunction with a policy using imaginary rollouts while implicitly regularizing the learned policy via appropriate parameter initialization and conservative trust-region learning updates. We evaluate BREMEN on standard offline RL benchmarks of high-dimensional continuous control tasks, where only a single static dataset is used. In this fixed-batch setting, our experiments show that BREMEN can not only achieve performance competitive with state-of-the-art when using standard dataset sizes but also learn with 10-20 times smaller datasets, which previous methods are unable to attain. Enabled by such stable and sample-efficient offline learning, we show that BREMEN can learn successful policies with only 5-10 deployments in the online setting, significantly outperforming existing off-policy and offline RL algorithms in deployment efficiency while keeping sample efficiency. + +# 2 PRELIMINARIES + +We consider a Markov Decision Process (MDP) setting, characterized by the tuple $\begin{array} { r l } { \mathcal { M } } & { { } = } \end{array}$ $( S , \mathcal { A } , p , r , \gamma )$ , where $s$ is the state space, $\mathcal { A }$ is the action space, $p ( s ^ { \prime } | s , a )$ is the transition probability distribution or dynamics, $r ( s )$ is the reward function and $\gamma \in ( 0 , 1 )$ is the discount factor. A policy $\pi$ is a function that determines the agent behavior, mapping from states to probability distributions over actions. The goal is to obtain the optimal policy $\pi ^ { * }$ , which maximizes the expectation of discounted sum of rewards. The transition probability $p ( s ^ { \prime } | s , a )$ is usually unknown, and estimated with a parameterized dynamics model $f _ { \phi }$ (e.g. a neural network) in model-based RL. For simplicity, we assume that the reward function $r ( s )$ is known, and the reward can be computed for any arbitrary state, but we may extend to the unknown setting and predict it using a parameterized function. + +On-policy vs Off-policy, Online vs Offline At a high-level, most RL algorithms alternate many times between collecting a batch of transitions (deployments) and optimizing the policy (learning). If the algorithms discard data after each policy update, they are on-policy (Schulman et al., 2015; 2017), while if they accumulate data in a buffer $\mathcal { D }$ , i.e. experience replay (Lin, 1992), they are off-policy (Mnih et al., 2015; Lillicrap et al., 2016; Gu et al., 2016; 2017b; Haarnoja et al., 2018; Fujimoto et al., 2019; Fakoor et al., 2019) because not all the data in buffer comes from the current policy. However, we consider all these algorithms to be online RL algorithms, since they involve many deployments during learning, ranging from hundreds to millions. On the other hand, in pure offline RL, one does not assume direct interaction and learns a policy from only a fixed dataset, which effectively corresponds to a single deployment allowed for learning. Classically, interpolating these two extremes were semi-batch RL algorithms (Lange et al., 2012; Singh et al., 1995), which improve the policy through repetitions of collecting a large batch of transitions $\mathcal { D } = \{ ( s , a , s ^ { \prime } , r ) \}$ and performing many or full policy updates. While these semi-batch RL also realize good deployment efficiency, they have not been extensively studied with neural network function approximators or in off-policy settings with experience replay for scalable sample-efficient learning. In our work, we aim to have both high deployment efficiency and sample efficiency by developing an algorithm that can solve the tasks with minimal policy deployments as well as transition samples. + +# 3 DEPLOYMENT EFFICIENCY + +Deploying a new policy for data collection can be associated with a number of costs and risks for many real-world applications like medicine, dialogue systems, or robotic control (Murphy et al., 2001; Mandel et al., 2014; Gu et al., 2017a; Kalashnikov et al., 2018; Nachum et al., 2019; Jaques et al., 2019). While there are abundant works on safety for RL (Chow et al., 2015; Eysenbach et al., 2018; Chow et al., 2018; Ray et al., 2019; Chow et al., 2019), they often do not provide guarantees in practice when combined with neural networks and stochastic optimization. It is therefore necessary to verify each policy before deployment (e.g. measuring the variance of rewards or checking out-of-bounds actions). Due to such costs associated with each deployment, it is desirable to minimize the number of distinct deployments needed during the learning process. Even ignoring safety considerations, frequent updates to a deployed policy can exacerbate communication bottlenecks in large-scale distributed RL systems, which are becoming more prevalent (Nair et al., 2015; Espeholt et al., 2018; 2019). We additionally discuss on the importance of the deployment efficiency in real-world applications. See Appendix C. + +In order to focus research on these practical bottlenecks, we propose a novel measure of RL algorithms, namely, deployment efficiency, which counts how many times the data-collection policy has been changed during improvement from random policy to solve the task. For example, if an RL algorithm operates by using its learned policy to collect transitions from the environment $I$ times, each time collecting a batch of $B$ new transitions, then the number of deployments is $I$ , while the total number of samples collected is $I \times B$ . The lower $I$ is, the more deployment-efficient the algorithm is; in contrast, sample efficiency looks at $I \times B$ . Online RL algorithms, whether they are on-policy or off-policy, typically update the policy and acquire new transitions by deploying the newly updated policy at every iteration. This corresponds to performing hundreds to millions of deployments during learning on standard benchmarks (Haarnoja et al., 2018), which is severely deployment inefficient. On the other hand, offline RL literature only studies the case of 1 deployment. A deployment-efficient algorithm would stand in the middle of these two extremes and ideally learn a successful policy from scratch while deploying only a few distinct policies, as illustrated in Figure 1. + +Recent deep RL literature seldom emphasizes deployment efficiency, with few exceptions in specific applications (Kalashnikov et al., 2018) where such a learning procedure is necessary. Deploymentinefficient algorithms will fail in scenarios where the deployment of each new policy is exorbitantly expensive, such as safety-critical robotics or user-facing products. Although current state-of-the-art algorithms on continuous control have substantially improved sample or data efficiency, they have not optimized for deployment efficiency. For example, SAC (Haarnoja et al., 2018), an efficient model-free off-policy algorithm, performs half a million to one million policy deployments during learning on MuJoCo (Todorov et al., 2012) benchmarks. ME-TRPO (Kurutach et al., 2018), a model-based algorithm, performs a much lower 100-300 policy deployments, although this is still relatively high for practical settings.2 In our work, we demonstrate successful learning on standard benchmark environments with only 5-10 deployments. + +# 4 BEHAVIOR-REGULARIZED MODEL-ENSEMBLE + +To achieve a favorable combination of both high deployment and sample efficiency, we propose Behavior-Regularized Model-ENsemble (BREMEN). BREMEN incorporates Dyna-style (Sutton, 1991; Kurutach et al., 2018) model-based RL, learning an ensemble of dynamics models in conjunction with a policy using imaginary rollouts and behavior regularization via conservative trust-region updates. + +# 4.1 IMAGINARY ROLLOUT FROM MODEL ENSEMBLE + +As in recent Dyna-style model-based RL methods (Kurutach et al., 2018; Wang et al., 2019), BREMEN uses an ensemble of $K$ deterministic dynamics models $\hat { f } _ { \phi } = \left\{ \hat { f } _ { \phi _ { 1 } } , \dots , \hat { f } _ { \phi _ { K } } \right\}$ to alleviate the problem of model bias. Each model $\hat { f } _ { \phi _ { i } }$ is parameterized by $\phi _ { i }$ and trained by the following objective, which minimizes mean squared error between the prediction of next state $\hat { f } _ { \phi _ { i } } \left( s _ { t } , a _ { t } \right)$ and true next state $s _ { t + 1 }$ over a dataset $\mathcal { D }$ : + +$$ +\operatorname* { m i n } _ { \phi _ { i } } \frac { 1 } { | \mathcal { D } | } \sum _ { \left( s _ { t } , a _ { t } , s _ { t + 1 } \right) \in \mathcal { D } } \frac { 1 } { 2 } \left. s _ { t + 1 } - \hat { f } _ { \phi _ { i } } \left( s _ { t } , a _ { t } \right) \right. _ { 2 } ^ { 2 } . +$$ + +During training of a policy $\pi _ { \theta }$ , imagined trajectories of states and actions are generated sequentially, using a dynamics model $\hat { f } _ { \phi _ { i } }$ that is randomly selected at each time step: + +$$ +a _ { t } \sim \pi _ { \theta } ( \cdot | \hat { s } _ { t } ) , \quad \hat { s } _ { t + 1 } = \hat { f } _ { \phi _ { i } } ( \hat { s } _ { t } , a _ { t } ) \quad \mathrm { w h e r e } \quad i \sim \{ 1 \cdot \cdot \cdot K \} . +$$ + +# 4.2 POLICY UPDATE WITH BEHAVIOR REGULARIZATION + +In order to manage the discrepancy between the true dynamics and the learned model caused by the distribution shift in batch settings, we propose to use iterative policy updates via a trust-region constraint, re-initialized with a behavior-cloned policy after every deployment. Specifically, after each deployment, we are given an updated dataset of experience transitions $\mathcal { D }$ . With this dataset, we approximate the true behavior policy $\pi _ { b }$ through behavior cloning (BC), utilizing a neural network $\hat { \pi } _ { \beta }$ parameterized by $\beta$ , where we implicitly assume a fixed variance, a common practice in BC (Rajeswaran et al., 2017): + +$$ +\operatorname* { m i n } _ { \beta } \frac { 1 } { | \mathscr { D } | } \sum _ { ( s _ { t } , a _ { t } ) \in \mathscr { D } } \frac { 1 } { 2 } \left. a _ { t } - \hat { \pi } _ { \beta } \left( s _ { t } \right) \right. _ { 2 } ^ { 2 } . +$$ + +After obtaining the estimated behavior policy, we initialize the target policy $\pi _ { \theta }$ as a Gaussian policy with mean from $\hat { \pi } _ { \beta }$ and standard deviation of 1. This BC initialization in conjunction with gradient descent based optimization may be seen as implicitly biasing the optimized $\pi _ { \theta }$ to be close to the data-collection policy (Nagarajan & Kolter, 2019), and thus works as a remedy for the distribution shift problem (Ross et al., 2011). To further bias the learned policy to be close to the data-collection + +# Algorithm 1 BREMEN for Deployment-Efficient RL + +
Input: Empty dataset Dau,D,Initial parameters Φ = {1,·,Φk},β,Number of policy optimization T
Numberof deploymentsI.
1:Randomly initialize the target policy πθ .
2:for deploymenti=1,·.,I do
3:Collect B transitions in the true environment using T and add them to dataset
Dall←DalU{St,at,rt,St+1},D←{st,at,rt,St+1}.
4:Train K dynamics models f using Dau via Equation 1.
5: 6:Train estimated behavior policy πβ using D by behavior cloning via Equation 3.
7:Re-initialize target policy πeo = Normal(β,1). for policy optimization k =1,..·,T do
8:Generate imaginary rollout via Equation 2.
9:Optimize target policy Tβ satisfying Equation 4 with the rollout.
+ +policy, we opt to use a KL-based trust-region optimization (Schulman et al., 2015). Therefore, the optimization of BREMEN becomes + +$$ +\begin{array} { r l } & { \theta _ { k + 1 } = \underset { \theta } { \arg \operatorname* { m a x } } \ \underset { s , a \sim \pi _ { \theta _ { k } } , \hat { f } _ { \phi _ { i } } } { \mathbb { E } } [ \frac { \pi _ { \theta } ( a | s ) } { \pi _ { \theta _ { k } } ( a | s ) } A ^ { \pi _ { \theta _ { k } } } ( s , a ) ] } \\ & { \mathrm { s . t . } \quad \underset { s \sim \pi _ { \theta _ { k } } , \hat { f } _ { \phi _ { i } } } { \mathbb { E } } [ D _ { \mathrm { K L } } ( \pi _ { \theta } ( \cdot | s ) | | \pi _ { \theta _ { k } } ( \cdot | s ) ) ] \leq \delta , \quad \pi _ { \theta _ { 0 } } = \mathrm { N o r m a l } ( \hat { \pi } _ { \beta } , 1 ) , } \end{array} +$$ + +where $A ^ { \pi _ { \theta _ { k } } } ( s , a )$ is the advantage of $\pi _ { \theta _ { k } }$ computed using model-based rollouts in the learned dynamics model and $\delta$ is the maximum step size. + +The combination of BC for initialization and finite iterative trust-region updates serves as an implicit KL regularization. This is in contrast to many previous offline RL algorithms that augment the value function with a penalty of explicit KL divergence (Siegel et al., 2020; Wu et al., 2019) or maximum mean discrepancy (Kumar et al., 2019). Empirically, we found that our regularization technique outperforms the explicit KL penalty (Section 5.3). Furthermore, we provide a mathematical intuition explaining how our methods works as an implicit regularization of distributional shift in Appendix A. + +By recursively performing offline procedure, BREMEN can be used for deployment-efficient learning as shown in Algorithm 1, starting from a randomly initialized policy, collecting experience data, and performing offline policy updates. + +# 5 EXPERIMENTS + +In order to realize a deployment-efficient RL algorithm, the batch policy optimizer has to be stable and sample-efficient. We first evaluate BREMEN in the offline setting, where the algorithm learns the policy from a static dataset. Standard benchmarks of MuJoCo physics simulator shown in $\mathrm { W u }$ et al., 2019) and more recent datasets (Fu et al., 2020) are used in the evaluation, and we compared the asymptotic performance of BREMEN with other offline RL methods including the concurrent model-based approaches. We then tested the sample-efficiency of offline algorithms using smaller datasets. We lastly extend the experiment to deployment-efficient settings, where the algorithms learn their policies from scratch via a limited number of deployments and perform some ablations to see how components in BREMEN affect performance. See Appendix F for further details. + +# 5.1 EVALUATING OFFLINE RL PERFORMANCES + +Standard Benchmarks We evaluate BREMEN on standard offline RL benchmarks following and identical protocol as in Wu et al. (2019): We first train online SAC to a certain cumulative reward threshold, 4,000 in HalfCheetah, 1,000 in Ant, Hopper, and Walker2d, and collect offline datasets. We evaluate agents with the offline dataset of one million (1M) transitions, which is standard for BCQ and BRAC. Table 1 (top) shows that BREMEN can achieve performance competitive with state-of-the-art model-free offline RL algorithms when using the standard dataset size of 1M. We also test BREMEN with more recent benchmarks of D4RL (Fu et al., 2020) and compared the performance with the existing model-free and model-based methods. See Appendix D for the results. + +
1,000,000(1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset BC1191 1321±141412611281376
4281±12 5783±2721341±161 1130±1271421±147 2153±753
BCQ2021±31 2072±2851422±90
BRAC7192±1152239±1124
BRAC (max Q)2369±2347320±911916±3432409±1210
BREMEN (Ours)3328±2758055±1032058±8522346±230
ME-TRPO (offline)1258±5501804±924518±91211±154
100,000(100K)transitions
MethodAntHalfCheetahHopperWalker2d
Dataset1191406611281376
BC1330±814266±211322±1091426±47
BCQ1363±1993915±4111129±2382187±196
BRAC-157±3832505±25011310±702162±1109
BRAC (max Q)-226±3872332±24221422±1012164±1114
BREMEN (Ours)1633±1276095±3702191±4552132±301
ME-TRPO (offline)974±42±434307±17010±61
50,000 (50K) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset1191413811281376
BC1270±654230±491249±611420±194
BCQ1329±951319±6261178±2351841±439
BRAC-878±244-597±731277±102976±1207
BRAC (max Q)-843±279-590±561276±225903±1137
BREMEN(Ours)1347±2835823±1461632±7962280±647
938±32
ME-TRPO (offfline)-73±95152±13176±343
+ +Table 1: Comparison of BREMEN to the existing offline methods on static datasets. Each cell shows the average cumulative reward and their standard deviation, where the number of samples is 1M, 100K, and 50K, respectively. The maximum steps per episode is 1,000. BRAC applies a primal form of KL value penalty, and BRAC (max Q) means its variant of sampling multiple actions and taking the maximum according to the learned Q function. + +Evaluating Sample-Efficiency We then evaluate the sample-efficiency by making much smaller datasets of $5 0 \mathrm { k }$ and $1 0 0 \mathrm { k }$ transitions $5 \sim 1 0 \%$ of Wu et al. (2019)). Surprisingly, Table 1 (middle and bottom) shows that BREMEN can also learn with smaller datasets, where BCQ and BRAC are unable to exceed even BC baseline. This is a novel evaluation protocol we proposed, and our BREMEN’s superior performance here is exactly what enables recursive BREMEN in the next section to be an effective algorithm in deployment-constrained settings. + +# 5.2 EVALUATING DEPLOYMENT EFFICIENCY IN ONLINE RL BENCHMARKS + +We compare BREMEN to ME-TRPO, SAC, BCQ, and BRAC applied to limited deployment settings. To adapt offline methods (BCQ, BRAC) to this setting, we simply apply them in a recursive fashion;3 at each deployment iteration, we collect a batch of data with the most recent policy and then run the offline update with this dataset. As for SAC, we simply change the replay buffer to update only at specific deployment intervals. For the sake of comparison, we align the number of deployments and the amount of data collection at each deployment (either $1 0 0 \mathrm { k }$ or $2 0 0 \mathrm { k }$ ) for all methods.4 + +Figure 2 shows the results with $2 0 0 \mathrm { k }$ (top) and $1 0 0 \mathrm { k }$ (bottom) batched transitions per deployment. Regardless of the environments and the batch size per update, BREMEN achieves remarkable performance while existing online and offline RL methods struggle to make any progress. As a point of comparison, we also include results for online SAC and ME-TRPO without deployment-limits but using the same number of transitions. We additionally compare BREMEN to the model-based offline RL methods with uncertainty-based penalties. See Appendix E for further details. + +Following the motivation of deployment efficiency, obtaining a successful policy under data-collection constraint conditions in the real application, we extensively evaluate our algorithm on more realistic robotics environments in OpenAI Gym. The experimental procedure is the same as above, while we limit the batch size at each deployment as only $2 5 \mathrm { k }$ . Figure 3 presents the reaching tasks with Fetch robot and 20-DoF shadow hand (Plappert et al., 2018), and the experimental results in both environments. Only BREMEN shows stable improvement and high performance, while other offline and online algorithms fail to learn. These results suggest that a model-based method is a desirable approach for satisfying practical requirements in robotics, i.e. sample and deployment efficiency. + +![](images/6a1cb8fc593fa991de860c81499864a36dc243a21b814426030744b691e27217.jpg) +Figure 2: Evaluation of BREMEN with the existing methods (ME-TRPO, SAC, BCQ, BRAC) under deployment constraints (to 5-10 deployments with batch sizes of 200k and 100k). The average cumulative rewards and their standard deviations with 5 random seeds are shown. Vertical dotted lines represent where each policy deployment and data collection happen. BREMEN is able to learn successful policies with only 5-10 deployments, while the state-of-the-art off-policy (SAC), model-based (ME-TRPO), and recursively-applied offline RL algorithms (BCQ, BRAC) often struggle to make any progress. For completeness, we show ME-TRPO(online) and SAC(online) which are their original optimal learning curves without deployment constraints, plotted with respect to samples normalized by the batch size. While SAC(online) substantially outperforms BREMEN in sample efficiency, it uses 1 deployment per sample, leading to 100k-500k deployments required for learning. Interestingly, BREMEN achieves even better performance than the original ME-TRPO(online), suggesting the effectiveness of implicit behavior regularization. For SAC and ME-TRPO under deployment-constrained evaluation, their batch size between policy deployments differs substantially from their standard settings, and therefore we performed extensive hyper-parameter search on the relevant parameters such as the number of policy updates between deployments, as discussed in Appendix F.2.1. + +![](images/aefe5703a6af1bb98f484da513d1f7861b5ff52440d53d4cfceab98875c791d8.jpg) +Figure 3: Robotics environments and the results under deployment constraints (10 deployments with batch sizes of 25k). The performances are averaged over 5 seeds. BREMEN seems the only method that shows both stable improvement and solving tasks without large degradation or sub-optimal convergence. + +# 5.3 ABLATION: EVALUATING EFFECTIVENESS OF IMPLICIT KL CONTROL + +In this section, we present an experiment to better understand the effect of BREMEN’s implicit regularization. Figure 4 shows the KL divergence of learned policies from the last deployed policy. We compare BREMEN to variants of BREMEN that use an explicit KL penalty on value instead of BC initialization (conservative KL trust-region updates are still used). We find that the explicit KL without behavior initialization variants learn policies that move farther away from the last deployed policy than behavior initialized policies. This suggests that the implicit behavior regularization employed by BREMEN is more effective as a conservative policy learning protocol. In addition, to assess the effect of repeated behavior cloning initialization, we also evaluate a variant of BREMEN without behavior cloning re-initialization (grey). This variant works in easier environments (Ant, Halfcheetah), but does not show remarkable progress in more challenging ones with termination (Hopper, Walker2d). + +![](images/caaaeaae5c063a15f89b51e7364e62582bf4f0db0e551d24fb5de280da818a2c.jpg) +Figure 4: We examine average cumulative rewards (top) and corresponding KL divergence between the last deployed policy and the target policy (bottom) with batch size 200K in limited deployment settings. The behavior initialized policy remains close to the last deployed policy during improvement without explicit value penalty $- \alpha D _ { \mathrm { K L } } ( { \bar { \pi _ { \theta } } } \| { \hat { \pi } } _ { \beta } )$ . The explicit penalty is controlled by a coefficient $\alpha$ . + +This result empirically supports the need for repeated behavior initialization after each deployment. +The results of further experiments are shown in Appendix G. + +# 6 RELATED WORK + +Deployment Efficiency and Offline RL Although we are not aware of any previous works which explicitly proposed the concept of deployment efficiency, its necessity in many real-world applications has been generally known. One may consider previously proposed semi-batch RL algorithms (Ernst et al., 2005; Lange et al., 2012; Singh et al., 1994; Roux, 2016) or theoretical analysis of switching cost under the tabular PAC-MDP settings (Bai et al., 2019; Guo & Brunskill, 2015) as approaching this issue. More recently, a related but distinct problem known as offline RL has gained popularity (Levine et al., 2020; Wu et al., 2019; Agarwal et al., 2019; Kumar et al., 2020). These works consider an extreme version of 1 deployment, and typically collect the static batch with a partially trained policy rather than a random policy. While offline RL has shown promising results for a variety of real-world applications, such as robotics (Mandlekar et al., 2019), dialogue systems (Jaques et al., 2019), or medical treatments (Gottesman et al., 2018), these algorithms struggle when learning a policy from scratch or when the dataset is small. Nevertheless, common themes of many offline RL algorithms – regularizing the learned policy to the behavior policy (Fujimoto et al., 2019; Kumar et al., 2019; Siegel et al., 2020; Wu et al., 2019) and utilizing ensembles to handle uncertainty (Kumar et al., 2019; Wu et al., 2019) – served as inspirations for the proposed our algorithm. A major difference of BREMEN from prior works is that the target policy is not explicitly forced to stick close to the estimated behavior policy through the policy update except for the initial iteration. Rather, BREMEN employs a more implicit regularization by initializing the learned policy with a behavior cloned policy and then applying conservative trust-region updates. Another major difference is the application of model-based approaches to fully offline settings, which has not been extensively studied in prior works (Levine et al., 2020), except the two concurrent works (Kidambi et al., 2020; Yu et al., 2020) that study pessimistic or uncertainty penalized MDPs with guarantees – closely related to Liu et al. (2019). By contrast, our work shows that a simple technique can already enable model-based offline algorithms to significantly outperform the prior model-free methods, and is, to the best of our knowledge, the first to define and extensively evaluate deployment efficiency with recursive experiments. + +Model-Based RL There are many types of model-based RL algorithms (Sutton, 1991; Deisenroth & Rasmussen, 2011; Heess et al., 2015). A simple algorithmic choice is Dyna-style (Sutton, 1991), which uses a parameterized model to estimate the true MDP transition function, stochastically mapping states and actions to next states. The dynamics model can then serve as a simulator of the environment during policy updates. Dyna-style algorithms often suffer from the distributional shift, also known as model bias, which leads RL agents to exploit regions where the data is insufficient, and significant performance degradation. A variety of remedies have been proposed to relieve the issue of model bias, such as the use of multiple dynamics models as an ensemble (Chua et al., 2018; Kurutach et al., 2018; Janner et al., 2019), meta-learning (Clavera et al., 2018), energy-based regularizer (Boney et al., 2019), game-theoretic framework (Rajeswaran et al., 2020), and explicit penalty for unknown states (Kidambi et al., 2020; Yu et al., 2020). Notably, we have employed a subset of these remedies – model ensembles and trust-region updates (Kurutach et al., 2018) – for BREMEN. Compared to prior works, our work is notable for using BC initialization in conjunction with trust-region updates to alleviate the distribution shift of the learned policy from the dataset used to train the dynamics model. + +# 7 CONCLUSION + +In this work, we introduced deployment efficiency, a novel measure for RL performance that counts the number of changes in the data-collection policy during learning. To enhance deployment efficiency, we proposed a novel model-based offline algorithm, Behavior-Regularized Model-ENsemble (BREMEN), combining model-ensembles with trust region updates from model-based RL literature (Kurutach et al., 2018), and policy initialization with behavior cloning from offline RL literature (Fujimoto et al., 2019; Wu et al., 2019). Crucially, BREMEN can improve policies offline sample-efficiently even when the batch size is 10-20 times smaller than prior works, allowing BREMEN to achieve impressive results in limited deployment settings, obtaining successful policies from scratch in only 5-10 deployments. Not only can this help alleviate costs and risks in real-world applications, but it can also reduce the amount of communication required during distributed learning and could form the basis for communication-efficient large-scale RL in contrast to prior works (Nair et al., 2015; Espeholt et al., 2018; 2019). Most critically, we show that under deployment efficiency constraints, most prior algorithms – model-free or model-based, online or offline – fail to achieve successful learning. One possible direction for future work is to incorporate verification efficiency into consideration, since a stochastic multi-modal policy could collect more diverse transitions while it takes more trajectories to be verified for safety than a uni-modal policy. While we presented promising results on some realistic simulated environments, validating BREMEN on real robots is another direction. We hope our work can gear the research community to value deployment efficiency as an important criterion for RL algorithms, and to eventually achieve similar sample efficiency and asymptotic performance as the state-of-the-art algorithms like SAC (Haarnoja et al., 2018) while having the deployment efficiency well-suited for safe and practical real-world reinforcement learning. + +# REFERENCES + +Fabian Abel, Yashar Deldjoo, Mehdi Elahi, and Daniel Kohlsdorf. Recsys challenge 2017: Offline and online evaluation. In ACM Conference on Recommender Systems, 2017. + +Rishabh Agarwal, Dale Schuurmans, and Mohammad Norouzi. An optimistic perspective on offline reinforcement learning. arXiv preprint arXiv:1907.04543, 2019. + +Christopher G. Atkeson, Benzun P. Wisely Babu, Nandan Banerjee, Dmitry Berenson, Christoper P. Bove, Xiongyi Cui, Mathew DeDonato, Ruixiang Du, Siyuan Feng, Perry Franklin, Michael Gennert, Joshua P. 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MOPO: Model-based offline policy optimization. arXiv preprint arXiv:2005.13239, 2020. + +# APPENDIX + +# A IMPLICIT KL CONTROL FROM A MATHEMATICAL PERSPECTIVE + +We can intuitively understand that behavior cloning initialization with trust-region updates works as a regularization of distributional shift, and this can be supported by theory. Following the notation of Janner et al. (2019), we denote the generalization error of a dynamics model on the state distribution under the true behavior policy as $\begin{array} { r } { \epsilon _ { m } = \operatorname* { m a x } _ { t } \mathbb { E } _ { s \sim d _ { t } ^ { \pi _ { b } } } D _ { T V } ( \bar { p ( } s _ { t + 1 } | s _ { t } , a _ { t } ) | | p _ { \phi } ( s _ { t + 1 } | s _ { t } , a _ { t } ) ) } \end{array}$ , where $D _ { T V }$ represents the total variation distance between true dynamics $p$ and learned model $p _ { \phi }$ . We also denote the distribution shift on the target policy as $\begin{array} { r } { \operatorname* { m a x } _ { s } D _ { T V } ( \pi _ { b } | | \pi ) \le \epsilon _ { \pi } } \end{array}$ . A bound relating the true returns $\eta [ \pi ]$ and the model returns $\hat { \eta } [ \pi ]$ on the target policy is given in Janner et al. (2019) as, + +$$ +\eta [ \pi ] \ge \hat { \eta } [ \pi ] - \left[ \frac { 2 \gamma r _ { m a x } ( \epsilon _ { m } + 2 \epsilon _ { \pi } ) } { ( 1 - \gamma ) ^ { 2 } } + \frac { 4 r _ { m a x } \epsilon _ { \pi } } { ( 1 - \gamma ) } \right] . +$$ + +This bound guarantees the improvement under the true returns as long as the improvement under the model returns increases by more than the slack in the bound due to $\epsilon _ { m } , \epsilon _ { \pi }$ (Janner et al., 2019; Levine et al., 2020). + +We may relate this bound to the specific learning employed by BREMEN, which includes dynamics model learning, behavior cloning policy initialization, and conservative KL-based trust-region policy updates. To do so, we consider an idealized version of BREMEN, where the expectations over states in equations Equation 1, 3, 4 are replaced with supremums and the dynamics model is set to have unit variance. + +Proposition 1 (Policy and model error bound). Suppose we apply the idealized BREMEN on a dataset $\mathcal { D }$ , and define $\epsilon _ { \beta } , \epsilon _ { \phi }$ in terms of the behavior cloning and dynamics model losses as, + +$$ +\begin{array} { r l } & { \epsilon _ { \beta } : = \underset { s } { \operatorname* { s u p } } \mathbb { E } _ { a \sim \mathcal { D } ( - | s ) } [ \| a - \hat { \pi } _ { \beta } \left( s \right) \| _ { 2 } ^ { 2 } / 2 ] - \mathcal { H } ( \pi _ { b } ( - | s ) ) } \\ & { \epsilon _ { \phi } : = \underset { s , a } { \operatorname* { s u p } } \mathbb { E } _ { s ^ { \prime } \sim \mathcal { D } ( - | s , a ) } \left[ \| s ^ { \prime } - \hat { f } _ { \phi } ( s , a ) \| _ { 2 } ^ { 2 } / 2 \right] - \mathcal { H } ( p ( - | s , a ) ) , } \end{array} +$$ + +where $\mathcal { H }$ denotes the Shannon entropy. If one then applies $T$ KL-based trust-region steps of step size $\delta$ (Equation 4) using stochastic dynamics models with mean $\hat { f } _ { \phi }$ and standard deviation $^ { l }$ , then + +$$ +\epsilon _ { \pi } = \sqrt { \frac { 1 } { 2 } \epsilon _ { \beta } + \frac { d _ { a } } { 4 } \log 2 \pi } + T \sqrt { \frac { 1 } { 2 } \delta } ; \epsilon _ { m } \leq \sqrt { \frac { 1 } { 2 } \epsilon _ { \phi } + \frac { d _ { s } } { 4 } \log 2 \pi } , +$$ + +where $d _ { a }$ and $d _ { s }$ denotes the dimension of action and state space. + +Proof. We first consider $\epsilon _ { \pi }$ . The behavior cloning objective in its supremum form is, + +$$ +\begin{array} { r c l } { { \epsilon _ { \beta } } } & { { = } } & { { \displaystyle \operatorname* { s u p } _ { s \in \mathcal { D } } \mathbb { E } _ { a \sim \mathcal { D } ( - | s ) } [ \| a - \hat { \pi } _ { \beta } \left( s \right) \| _ { 2 } ^ { 2 } / 2 ] - \mathcal { H } ( \pi _ { b } ( - | s ) ) } } \\ { { } } & { { } } & { { \displaystyle = } } & { { \displaystyle \operatorname* { s u p } _ { s \in \mathcal { D } } \mathbb { E } _ { a \sim \mathcal { D } ( - | s ) } \left[ - \log \pi _ { \theta _ { 0 } } ( a | s ) \right] - \mathcal { H } ( \pi _ { b } ( - | s ) ) - \frac { d _ { a } } { 2 } \log 2 \pi } } \\ { { } } & { { } } & { { \displaystyle = } } & { { \displaystyle \operatorname* { s u p } _ { s \in \mathcal { D } } D _ { K L } ( \pi _ { b } ( - | s ) | | \pi _ { \theta _ { 0 } } ( - | s ) ) - \frac { d _ { a } } { 2 } \log 2 \pi . } } \end{array} +$$ + +We apply Pinsker’s inequality to the true and estimated behavior policy to yield + +$$ +\operatorname* { s u p } _ { s } D _ { T V } ( \pi _ { b } ( - | s ) | | \pi _ { \theta _ { 0 } } ( - | s ) ) \leq { \sqrt { { \frac { 1 } { 2 } } \epsilon _ { \beta } + { \frac { d _ { a } } { 4 } } \log 2 \pi } } . +$$ + +By the same Pinsker’s inequality, we have, + +$$ +\operatorname* { s u p } _ { s } D _ { T V } \big ( \pi _ { \theta _ { k } } ( - | s ) | | \pi _ { \theta _ { k + 1 } } ( - | s ) \big ) \leq \sqrt { \delta / 2 } . +$$ + +Therefore, by triangle inequality, we have + +$$ +\operatorname* { s u p } _ { s } D _ { T V } ( \pi _ { b } ( - | s ) | | \pi _ { \theta _ { T } } ( - | s ) ) \leq \sqrt { \frac { 1 } { 2 } \epsilon _ { \beta } + \frac { d _ { a } } { 4 } \log { 2 \pi } } + T \sqrt { \frac { 1 } { 2 } \delta } = \epsilon _ { \pi } , +$$ + +as desired. + +We perform similarly for $\epsilon _ { m }$ . The model dynamics loss is + +$$ +\begin{array} { r c l } { { \epsilon _ { \phi } } } & { { = } } & { { \displaystyle \operatorname* { s u p } _ { s , a } \mathbb { E } _ { s ^ { \prime } \sim \mathcal { D } ( - | s , a ) } \left[ \| s ^ { \prime } - \hat { f } _ { \phi } ( s , a ) \| _ { 2 } ^ { 2 } / 2 \right] - \mathcal { H } ( p ( - | s , a ) ) } } \\ { { } } & { { } } & { { } } \\ { { \displaystyle = } } & { { \displaystyle \operatorname* { s u p } _ { s , a } \mathbb { E } _ { s ^ { \prime } \sim \mathcal { D } ( - | s , a ) } \left[ - \log p _ { \phi } ( s ^ { \prime } | s , a ) \right] - \mathcal { H } ( p ( - | s , a ) ) - \frac { d _ { s } } { 2 } \log 2 \pi } } \\ { { } } & { { } } & { { } } \\ { { \displaystyle = } } & { { \displaystyle \operatorname* { s u p } _ { s , a } D _ { K L } ( p ( - | s , a ) | | p _ { \phi } ( - | s , a ) ) - \frac { d _ { s } } { 2 } \log 2 \pi . } } \end{array} +$$ + +We apply Pinsker’s inequality to the true dynamics and learned model to yield + +$$ +\epsilon _ { m } \leq \operatorname* { s u p } _ { s , a } D _ { T V } ( p ( - | s , a ) | | p _ { \phi } ( - | s , a ) ) \leq \sqrt { \frac { 1 } { 2 } \epsilon _ { \phi } + \frac { d _ { s } } { 4 } \log 2 \pi } , +$$ + +as desired. + +# B TRADE-OFF BETWEEN SAMPLE AND DEPLOYMENT EFFICIENCY + +An important aspect of deployment efficiency is the trade-off between sample and deployment efficiency. To collect multiple data points per experiment and show this trade-off, we run recursive BREMEN with different batch sizes, and record how many samples are required to cross different reward thresholds. + +HalfCheetah (Reward 7,000 result) and other results from Figure 5 generally show that high deployment efficiency lowers sample efficiency, confirming the inherent trade-off. However, in rare cases, e.g. Ant (Reward 5,000 result), it could be possible to achieve both high deployment efficiency and high sample efficiency through the right choice of the batch size hyper-parameter. + +![](images/e4a79595f8df889828b941ec6d05aca10bd9f4d0a7a9a704b384c7c841649438.jpg) +Figure 5: From the view of both sample and deployment efficiency at certain cumulative reward threshold, we evaluate BREMEN in Ant (left) and HalfCheetah (right). x and y axes respectively represent the number of samples and the number of deployments.Each data point comes from running BREMEN with different reward thresholds and batch sizes. The numbers above the points (e.g. 1000, 2000, ...) represent the reward threshold. The results (especially, reward 7,000 threshold in HalfCheetah) generally show that high deployment efficiency lowers sample efficiency, confirming the inherent trade-off. + +# C DISCUSSION: IMPORTANCE OF DEPLOYMENT EFFICIENCY IN REAL-WORLD APPLICATIONS + +Our notion of deployment-efficiency is necessitated by cost and safety constraints typical in many real world scenarios. Namely, a common approach to real-world applications (Cabi et al., 2020; DulacArnold et al., 2019; Kalashnikov et al., 2018) is the following iterative training and data-collection paradigm: + +1. Aggregate past previous dataset from worker(s) +2. Update policy based on the collected data +3. Deploy the policy to the worker(s) +4. Monitor the policy works as expected e.g. checking if it does not violate safety criterion +(this safety verification step may alternatively happen before step 3) +5. Let the worker(s) collect experiences with the latest policy. + +It is easy to see that the number of deployments is a critical bottleneck, as it involves both monitoring of the policy (Step 4) and communication to the workers (Step 3), and both of these steps can incur significant cost. Specifically, Step 4 requires evaluating the policy for safety, and often requires human monitors (Atkeson et al., 2015). As for Step 3, communication to workers can also be a bottleneck, especially in highly-parallelized distributed RL systems (Nair et al., 2015; Espeholt et al., 2018; 2019). Every policy deployment requires a potentially expensive communication between different machines/processes, and this can be a bottleneck on the whole system. + +As a concrete example of the necessity of good deployment efficiency, consider optimization of personalization in web apps or recommender systems (Abel et al., 2017). Once a policy is learned on a batch of past experiences, it is deployed to a collection of web-hosting servers. In this scenario, both safety and communication concerns are relevant: Safety of the new policy is typically ensured by initially deploying the policy to a small percentage of users; after monitoring the results for some length of time (e.g. the newly deployed policy does not deteriorate user experiences), one can expand the target user set. As for communication, deploying a new policy to web-hosting servers can be time intensive, especially in large-scale web applications where the policy must be deployed to a network of servers around the world. Thus, in this setting, it is clear that online updating of the policy is infeasible due to both safety and communication constraints. Accordingly, the deployment-efficiency of any candidate RL algorithm is of tantamount importance. + +The safe exploration might be mentioned as a potential alternative to deployment-efficiency. While safe exploration can arguably tackle the first concern above (safety risks of the policy), it does nothing to mitigate the latter (the engineering or communication costs associated with online deployment of a policy). Furthermore, this still ignores the fact that in many scenarios the ability to do safe exploration is not a given. While some safe RL algorithms can provide guarantees in tabular cases, these guarantees no longer hold when using function approximation with neural networks (Chow et al., 2018). In these cases, it can be much more difficult to perform “safe exploration” than it is to develop a deployment-efficient algorithm. + +# D EVALUATING OFFLINE PERFORMANCES ON D4RL DATASETS + +We compare BREMEN to MOPO (Yu et al., 2020), concurrently proposed model-based offline methods penalized by model epistemic uncertainty, and state-of-the-art model-free offline algorithms, namely, CQL (Kumar et al., 2020), BEAR (Kumar et al., 2019), BRAC (Wu et al., 2019), AWR (Peng et al., 2019) and BCQ (Fujimoto et al., 2019), on the D4RL MuJoCo locomotion datasets (Fu et al., 2020), used as standard offline RL benchmarks (Kumar et al., 2020; Nair et al., 2020). They have several types of offline data collected with different strategies. We choose the hyper parameters of BREMEN in Section 5.1 and F.2.2. Table 2 shows BREMEN beats recent state-of-the-art algorithms with the highest normalized score (around 100 corresponds to an expert) in several tasks, while none of the methods consistently achieves the best performance. This result suggests that the implicit regularization with the model-based method performs surprisingly well in offline settings despite of its simplicity. + +
Task NameBCBREMENMOPOCQLBEARBRAC-vAWRBCQ
halfcheetah-randomwalker2d-randomhopper-random2.11.69.836.93.712.231.913.013.335.47.025.17.311.431.21.912.22.51.510.22.24.910.6
10.8
halfcheetah-mediumwalker2d-mediumhopper-medium36.16.629.055.059.669.340.214.026.544.479.258.041.759.152.146.381.131.137.417.435.940.753.154.5
halfcheetah-medium-replaywalker2d-medium-replayhopper-medium-replay38.411.311.847.27.624.154.042.792.546.238.619.233.747.70.90.640.315.528.438.2
26.748.615.033.1
halfcheetah-medium-expertwalker2d-medium-experthopper-medium-expert35.86.4111.953.355.264.657.955.051.762.498.7111.053.440.196.341.981.60.852.753.827.164.757.5110.9
+ +Table 2: Evaluation on D4RL MuJoCo locomotion datasets. The normalized score of BREMEN are averaged over 4 random seeds. We refer the score of MOPO (Yu et al., 2020) and CQL (Kumar et al., 2020) from their original papers. Other results are cited from Fu et al. (2020). BREMEN achieves the best and competitive score in several domains, while none of the algorithms beats all other methods. + +# E INCORPORATING PESSIMISTIC MODEL-BASED OFFLINE METHODS INTO BREMEN + +The concurrent model-based offline RL methods prescribe the use of uncertainty-based penalties (Kidambi et al., 2020; Yu et al., 2020), which can be incorporated into BREMEN. We therefore augmented BREMEN with either a hard (MOReL-like, green) or soft (MOPO-like, orange) reward penalty according to model uncertainty. MOReL quantifies the uncertainty measuring the maximum discrepancy of the prediction across the ensembles of the models and receives constant negative reward (-5.0 in our experiments) if the discrepancy is larger than the threshold (we set 3.0). MOPO measures the uncertainty by the maximum standard deviation of the model ensembles and uses this as a reward penalty with a coefficient (0.1 in our experiments). Evaluations in Figure 6 reveal that the soft reward penalty has notable results in Hopper and Walker2d, where model uncertainty is more crucial due to the episode’s termination. Hard reward penalty seems overly pessimistic in deployment-efficient settings. + +![](images/b92db87a8488301afcc0d533a6528c154563a870085080d2776b335a16c289e9.jpg) +Figure 6: Comparison to the pessimistic reward shaping incorporated into BREMEN. Soft reward penalty (MOPO-like, orange) performs well in the environments where the incomplete models appear to be fatal. + +# F DETAILS OF EXPERIMENTAL SETTINGS + +# F.1 IMPLEMENTATION DETAILS + +For our baseline methods, we use the open-source implementations of SAC, BC, BCQ, and BRAC published in Wu et al. (2019). SAC and BRAC have (300, 300) Q-Network and (200, 200) policy network. BC has (200, 200) policy network, and BCQ has (300, 300) Q-Network, (300, 300) policy network, and (750, 750) conditional VAE. As for online ME-TRPO, we utilize the codebase of model-based RL benchmark (Wang et al., 2019). BREMEN and online ME-TRPO use the policy consisting of two hidden layers with 200 units. The dynamics model also consists of two hidden layers with 1,024 units. We use Adam (Kingma & Ba, 2014) as the optimizer with the learning rate of 0.001 for the dynamics model, and 0.0005 for behavior cloning in BREMEN. Especially in BREMEN and online ME-TRPO, we adopt a linear feature value function to stabilize the training. BREMEN in deployment-efficient settings takes about two or three hours per deployment on an NVIDIA TITAN V. + +To leverage neural networks as Dyna-style (Sutton, 1991) dynamics models, we modify reward and termination function so that they are not dependent on the internal physics engine for calculation, following model-based benchmark codebase (Wang et al., 2019); see Table 3. Note that the score of baselines (e.g., BCQ, BRAC) is slightly different from Wu et al. (2019) due to this modification of the reward function. We re-run each algorithm in our environments and got appropriate convergence. + +The maximum length of one episode is 1,000 steps without any termination in Ant and HalfCheetah; however, termination function is enabled in Hopper and Walker2d. The batch size of transitions for policy update is 50,000 in BREMEN and ME-TRPO, following Kurutach et al. (2018). The batch size of BC and BRAC is 256, and BCQ is 100, also following Wu et al. (2019). + +![](images/22074d9a93978e2e7c0e5f01935d55d8e4c33f912df142778c7e453a465f0dca.jpg) +Figure 7: Four standard MuJoCo benchmark environments used in our experiments. + +
EnvironmentRewardfunctionTerminationinrollouts
Antxt -0.1||atl²2-3.0 × (zt -0.57)² +1False
HalfCheetahxt -0.1||atll2False
Hopperxt - 0.001||atl2²+1True
Walker2dxt-0.001||atl2+1True
+ +Table 3: Reward function and termination in rollouts in the experiments. We remove all contact information from observation of Ant, basically following Wang et al. (2019). + +# F.2 HYPER PARAMETERS + +In this section, we describe the hyper-parameters in both deployment-efficient RL (Section F.2.1) and offline RL (Section F.2.2) settings. We run all of our experiments with five random seed, and the results are averaged. + +# F.2.1 DEPLOYMENT-EFFICIENT RL + +Table 4 shows the hyper-parameters of BREMEN. The rollout length is searched from {250, 500, $1 0 0 0 \}$ , and max step size $\delta$ is searched from {0.001, 0.01, 0.05, 0.1, 1.0}. As for the discount factor $\gamma$ and GAE $\lambda$ , we follow Wang et al. (2019). + +
ParameterAntHalfCheetahHopperWalker2d
Iteration per batch2,0002,0006.0002,000
Deployment551010
Total iteration10.00010.00060.00020.000
Rollouts length2502501,0001,000
Max step size δ0.050.10.050.05
Discount factor y0.990.990.990.99
GAE入0.970.950.950.95
Stationary noise o0.10.10.10.1
+ +Table 4: Hyper-parameters of BREMEN in deployment-efficient settings. + +Number of Iterations for Policy Optimization To achieve high deployment efficiency, the number of iterations for policy optimization between deployments is one of the important hyper-parameters for fast convergence. In the existing methods (BCQ, BRAC, SAC), we search over three values: {10,000, 50,000, 100,000}, and choose 10,000 in BCQ and BRAC, and 100,000 in SAC (Figure 8). For BREMEN, we also search over three values: {2,000, 4,000, 6,000}. Figure 9 shows the results of iteration search, and we choose 2,000 in Ant, HalfCheetah, and Walker2d, and 6,000 in Hopper. + +![](images/e336bd4ed3f1cc2665e6fc99ab776b4c797ca110856fae70c3856d98bed9c733.jpg) +Figure 8: Search on the number of iterations for SAC policy optimization between deployments. The number of transitions per one data-collection is $2 0 0 \mathrm { K }$ . + +![](images/e3aa31a1dfb8de492f2a7d1dd0ba0b09d7546b19b72131e2fcba0161b0bbc2a1.jpg) +Figure 9: Search on the number of iterations for BREMEN policy optimization between deployments. The number of transitions per one data-collection is 200K. + +Stationary Noise in BREMEN To achieve effective exploration, the stochastic Gaussian policy is a good choice. We found that adding stationary Gaussian noise to the policy in the imaginary trajectories and data collection led to the notable improvement. Stationary Gaussian policy is written as, + +$$ +a _ { t } = \operatorname { t a n h } ( \mu _ { \theta } ( s _ { t } ) ) + \epsilon , \qquad \epsilon \sim \mathcal { N } ( 0 , \sigma ^ { 2 } ) . +$$ + +Another choice is a learned Gaussian policy, which parameterizes not only $\mu _ { \theta }$ but also $\sigma _ { \theta }$ . Learned gaussian policy is also written as, + +$$ +a _ { t } = \operatorname { t a n h } ( \mu _ { \theta } ( s _ { t } ) ) + \sigma _ { \theta } ( s _ { t } ) \odot \epsilon , \qquad \epsilon \sim \mathcal { N } ( 0 , \sigma ^ { 2 } ) . +$$ + +We utilize the zero-mean Gaussian ${ \mathcal { N } } ( 0 , \sigma ^ { 2 } )$ , and tune up $\sigma$ in Figure 10 with HalfCheetah, comparing stationary and learned strategies. From this experiment, we found that the stationary noise, the scale of 0.1, consistently performs well, and therefore we used it for all our experiments. + +![](images/e7fbb1985511ad7e639f10932800c9a46a2e1ab41d3aa44609db46b5b84b8f7d.jpg) +Figure 10: Search on the Gaussian noise parameter $\sigma$ in HalfCheetah. The number of transitions per one data-collection is 200K. + +Other Hyper-parameters in the Existing Methods As for online ME-TRPO, we collect 3,000 steps through online interaction with the environment per 25 iterations and split these transitions into a 2-to-1 ratio of training and validation dataset for learning dynamics models. In batch size 100,000 settings, we collect 2,000 steps and split with 1-to-1 ratio. Totally, we iterate 12,500 times policy optimization, which is equivalent to 500 deployments of the policy. Note that we carefully tune up the hyper-parameters of online ME-TRPO, and the performance is improved from Wang et al. (2019). + +Table 5 and Table 6 shows the tunable hyper-parameters of BCQ and BRAC, respectively. We refer Wu et al. (2019) to choose these values. In this work, BRAC applies a primal form of KL value penalty, and BRAC (max Q) means sampling multiple actions and taking the maximum according to the learned Q function. + +Table 5: Hyper-parameters of BCQ. + +
ParameterAntHalfCheetahHopperWalker2d
Policy learning rate3e-053e-043e-063e-05
Perturbation range Φ0.150.50.150.15
+ +Table 6: Hyper-parameters of BRAC. + +
ParameterAntHalfCheetahHopperWalker2d
Policy learning rate1e-41e-33e-51e-5
Divergence penalty α0.30.10.30.3
+ +# F.2.2 OFFLINE RL + +In the offline experiments, we apply the same hyper-parameters as in the deployment-efficient settings described above, except for the iteration per batch. Algorithm 2 is pseudocode for BREMEN in offline RL settings where policies are updated only with one fixed batch dataset. The number of iteration $T$ is set to 6,250 in BREMEN, and 500,000 in BC, BCQ, and BRAC. + +The datasets for $5 0 \mathrm { k }$ or $1 0 0 \mathrm { k }$ experiments are sliced from the beginning of the 1M batched datasets without shuffling, but we observed that the distribution of rewards in 50k or $1 0 0 \mathrm { k }$ is not different from 1M. + +# Algorithm 2 BREMEN for Offline RL + +Input: Offline dataset $\mathcal { D } = \{ s _ { t } , a _ { t } , r _ { t } , s _ { t + 1 } \}$ , Initial parameters $\phi = \{ \phi _ { 1 } , \cdot \cdot \cdot , \phi _ { K } \}$ , $\beta$ , Number of policy optimization $T$ . +1: Train $K$ dynamics models $\hat { f } _ { \phi }$ using $\mathcal { D }$ via Equation 1. +2: Train estimated behavior policy $\hat { \pi } _ { \beta }$ using $\mathcal { D }$ by behavior cloning via Equation 3. +3: Initialize target policy $\pi _ { \theta _ { 0 } } = \mathrm { N o r m a l } ( \hat { \pi } _ { \beta } , 1 )$ . +4: for policy optimization $k = 1 , \cdots , T$ do +5: Generate imaginary rollout. +6: Optimize target policy $\pi \theta$ satisfying Equation 4 with the rollout. + +# G ADDITIONAL EXPERIMENTAL RESULTS + +G.1 PERFORMANCE ON THE DATASET WITH DIFFERENT NOISE + +Following Wu et al. (2019) and Kidambi et al. (2020), we additionally compare BREMEN in offline settings to the other baselines (BC, BCQ, BRAC) with five datasets of different exploration noise. Each dataset has also one million transitions. + +• eps1: $40 \%$ of the dataset is collected by data-collection policy (partially trained SAC policy) $\pi _ { b }$ , $40 \%$ of the dataset is collected by epsilon greedy policy with $\epsilon = 0 . 1$ to take a random action, and $20 \%$ of dataset is collected by an uniformly random policy. +• eps3: Same as eps1, $40 \%$ of the dataset is collected by $\pi _ { b }$ , $40 \%$ is collected by epsilon greedy policy with $\epsilon = 0 . 3$ , and $20 \%$ is collected by an uniformly random policy. gaussian1: $40 \%$ of the dataset is collected by data-collection policy $\pi _ { b }$ , $40 \%$ is collected by the policy with adding zero-mean Gaussian noise $\mathcal { N } ( 0 , 0 . \bar { 1 } ^ { 2 } )$ to each action sampled from $\pi _ { b }$ , and $20 \%$ is collected by an uniformly random policy. +• gaussian3: $40 \%$ of the dataset is collected by data-collection policy $\pi _ { b }$ , $40 \%$ is collected by the policy with zero-mean Gaussian noise $\bar { \mathcal { N } ( 0 , 0 . 3 ^ { 2 } ) }$ , and $20 \%$ is collected by an uniformly random policy. +• random: All of the dataset is collected by an uniformly random policy. + +Table 7 shows that BREMEN can also achieve performance competitive with state-of-the-art modelfree offline RL algorithm even with noisy datasets. The training curves of each experiment are shown in Appendix G.4. + +# G.2 COMPARISON AMONG DIFFERENT NUMBER OF ENSEMBLES + +To deal with the distribution shift during policy optimization, also known as model bias, we introduce the dynamics model ensembles. We validate the performance of BREMEN with a different number of dynamics models $K$ . Figure 11 and Figure 12 show the performance of BREMEN with the different number of ensembles in deployment-efficient and offline settings. Ensembles with more dynamics models resulted in better performance due to the mitigation of distributional shift except for $K = 1 0$ , and then we choose $K = 5$ . + +![](images/6a0b7f3bfe2cb62d53bb5b1256c8a3eb377aa3e705d405e2f33cc4f47577999d.jpg) +Figure 11: Comparison of the number of dynamics models in deployment-efficient settings. + +![](images/4755817929bd8db982519e32692cfd6b1d33c3aabe852221237d9bf32a39226b.jpg) +Figure 12: Comparison of the number of dynamics models in offline settings. + +
Noise: eps1,1,000,000 (1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset10772936791815
BC1381±713788±740266±4861185±155
BCQ1937±1166046±276800±659479±537
BRAC2693±1557003±1181243±1623204±103
BRAC (max Q)2907±987070±811488±3863330±147
BREMEN (Ours)3519±1297585±4252818±761710±429
ME-TRPO (offline)1514±5031009±7311301±654128±153
+ +Noise: eps3, 1,000,000 (1M) transitions + +
MethodAntHalfCheetahHopperWalker2d
Dataset BC BCQ BRAC936 1364±121 1938±21 2718±90 2913±872408 2877±797 5739±188 6434±147662 519±532 1170±446 1224±71648 1066±176 1018±1231 2921±101
+ +Noise: gaussian1, 1,000,000 (1M) transitions + +
MethodAntHalfCheetahHopperWalker2d
Dataset107231508821070
BC1279±804142±18931±161137±477
BCQ1958±765854±498475±416608±416
BRAC2905±817026±1681456±1613030±103
BRAC (max Q)2910±1577026±1681575±893242±97
BREMEN (Ours)2912±1657928±3131999±6171402±290
ME-TRPO (offline)1275±6561275±656909±631171±119
+ +
Noise:gaussian3,1,0oo,0oo (1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset10582872781981
BC1300±344190±69611±4671217±361
BCQ1982±975781±5431137±582258±286
BRAC3084±1803933±27401432±4993253±118
BRAC (max Q)2916±993997±27611417±2673372±153
BREMEN (Ours)3432±1858124±1451867±3542299±474
ME-TRPO (offline)1237±3102141±872973±243219±145
+ +Noise: random, 1,000,000 (1M) transitions + +
MethodAntHalfCheetahHopperWalker2d
Dataset470-285342
BC989±10-2±1106±62108±110
BCQ1222±1142887±242206±7228±12
BRAC1057±923449±259227±3029±54
BRAC (max Q)683±573418±171224±3726±50
BREMEN (Ours)905±113627±193270±68254±6
ME-TRPO (offline)2221±6652701±120321±29262±13
+ +Table 7: Comparison of BREMEN to the existing offline methods in offline settings, namely, BC, BCQ (Fujimoto et al., 2019), and BRAC (Wu et al., 2019). Each cell shows the average cumulative reward and their standard deviation with 5 seeds. The maximum steps per episode is 1,000. Five different types of exploration noise are introduced during the data collection, eps1, eps3, gaussian1, gaussian3, and random. BRAC applies a primal form of KL value penalty, and BRAC (max Q) means sampling multiple actions and taking the maximum according to the learned Q function. + +# G.3 IMPLICIT KL CONTROL IN OFFLINE SETTINGS + +Similar to Section 5.3, we present offline RL experiments to better understand the effect of implicit KL regularization. In contrast to the implicit KL regularization with Equation 4, the optimization of BREMEN with explicit KL value penalty becomes + +$$ +\begin{array} { r l } & { \theta _ { k + 1 } = \underset { \theta } { \arg \operatorname* { m a x } } \ \underset { s , a \sim \pi _ { \theta _ { k } } , \hat { f } _ { \phi _ { i } } } { \mathrm { E } } [ \frac { \pi _ { \theta } ( a | s ) } { \pi _ { \theta _ { k } } ( a | s ) } ( A ^ { \pi _ { \theta _ { k } } } ( s , a ) - \alpha D _ { \mathrm { K L } } ( \pi _ { \theta } ( \cdot | s ) | ) \hat { \pi } _ { \beta } ( \cdot | s ) ) ) ] } \\ & { \quad \mathrm { s . t . } \quad \underset { s \sim \pi _ { \theta _ { k } } } { \mathrm { E } } [ D _ { \mathrm { K L } } ( \pi _ { \theta } ( \cdot | s ) | | \pi _ { \theta _ { k } } ( \cdot | s ) ) ] \leq \delta , } \end{array} +$$ + +where $A ^ { \pi _ { \theta _ { k } } } ( s , a )$ is the advantage of $\pi _ { \theta _ { k } }$ computed using imaginary rollouts with the learned dynamics model and $\delta$ is the maximum step size. Note that BREMEN with explicit KL penalty does not utilize behavior cloning initialization. + +We empirically conclude that the explicit constraint $- \alpha D _ { \mathrm { K L } } \big ( \pi _ { \boldsymbol { \theta } } \big ( \cdot | \boldsymbol { s } \big ) \big | \big | \hat { \pi } _ { \boldsymbol { \beta } } \big ( \cdot | \boldsymbol { s } \big ) \big )$ is unnecessary and just TRPO update with behavior-initialization as implicit regularization is sufficient in BREMEN algorithm. Figure 13 shows the KL divergence between learned policies and the last deployed policies (top row) and model errors measured by a mean squared error of predicted next state from the true state (second row). We find that behavior initialized policy with conservative KL trust-region updates well stuck to the last deployed policy during improvement without explicit KL penalty. The policy initialized with behavior cloning also tended to suppress the increase of model error, which implies that behavior initialization alleviates the effect of the distribution shift. In Walker2d, the model error of BREMEN is relatively large, which may relate to the poor performance with noisy datasets in Section G.1. + +![](images/380b79685657ca35961a182d8249d87b52383e893929db691d571c0225df1788.jpg) +Figure 13: Average cumulative rewards (top row) and corresponding KL divergence of learned policies from the last deployed policy (second row) and model errors (bottom row) in offline settings with 1M dataset (no noise). Behavior initialized policy (purple line) tends to suppress the policy and model error during training better than no-initialization (red line) or explicit KL penalty (green line). + +# G.4 TRAINING CURVES FOR OFFLINE RL WITH DIFFERENT NOISES + +In this section, we present training curves of our all experiments in offline settings. Figure 14 shows the results in Section 5.1. Figure 15, 16, 17, 18, and 19 also show the results in Section G.1. + +![](images/c5d8d3e93857b4772c71f9250ddb7e71a41d48a084aa8ff5d13896dcd60f0009.jpg) +Figure 14: Performance in Offline RL experiments (Table 1). (top row) dataset size is 1M, (second row) 100K, and (bottom row) 50K, respectively. Note that $\mathbf { X }$ -axis is the number of iterations with policy optimization in a log-scale. + +![](images/d9bc704351f20f3bf3fe30910804c40f1535b0cbc6b7b20c34aaf8f4523b2285.jpg) +Figure 15: Performance in Offline RL experiments with $\epsilon$ -greedy dataset noise $\epsilon = 0 . 1$ . Dataset size is 1M. + +![](images/f7f775ecb6dd3a924b4eb9058d7436ed3071014842ad90e854f68d8851a101b6.jpg) +Figure 16: Performance in Offline RL experiments with $\epsilon$ -greedy dataset noise $\epsilon = 0 . 3$ . Dataset size is 1M. + +![](images/130499bcf5e465aeeb59cee68e4a26cc2b0724c07bdd0d5ddaf94eaa44e62ee8.jpg) +Figure 17: Performance in Offline RL experiments with gaussian dataset noise $\mathcal { N } ( 0 , 0 . 1 ^ { 2 } )$ . Dataset size is 1M. + +![](images/b5e14c327508062c360ef17f8d7d6f8358413758c78deda33a2faba939bb6d82.jpg) +Figure 18: Performance in Offline RL experiments with gaussian dataset noise $\mathcal { N } ( 0 , 0 . 3 ^ { 2 } )$ . Dataset size is 1M. + +![](images/e8bd3de5b194349afabaa366a65cff854f71e8cdf7495f71533961a224245881.jpg) +Figure 19: Performance in Offline RL experiments with completely random behaviors. Dataset size is 1M. + +# G.5 DEPLOYMENT-EFFICIENT RL EXPERIMENT WITH DIFFERENT REWARD FUNCTION + +In addition to the main results in Section 5.2 (Figure 2), we also evaluate BREMEN in deploymentefficient setting with different reward function. We modified HalfCheetah environment into the one similar to cheetah-run task in Deep Mind Control Suite.5 The reward function is defined as + +$$ +r _ { t } = \left\{ \begin{array} { l l } { 0 . 1 \dot { x } _ { t } } & { ( 0 \leq \dot { x } _ { t } \leq 1 0 ) } \\ { 1 } & { ( \dot { x } _ { t } > 1 0 ) , } \end{array} \right. +$$ + +and the termination is turned off. Figure 20 shows the performance of BREMEN and existing methods. BREMEN also shows better deployment efficiency than other existing offline methods and online ME-TRPO, except for SAC, which is the same trend as that of main results. + +![](images/dd467a13475aaa5cb2f106904be422eee8725c7d1362d2167e7a9ddb7c8b3d1c.jpg) +Figure 20: Performance in Deployment-Efficient RL experiments with different reward function of HalfCheetah. \ No newline at end of file diff --git a/parse/train/3hGNqpI4WS/3hGNqpI4WS_content_list.json b/parse/train/3hGNqpI4WS/3hGNqpI4WS_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ce118d7571152e30a53322526f188d8f915536f4 --- /dev/null +++ b/parse/train/3hGNqpI4WS/3hGNqpI4WS_content_list.json @@ -0,0 +1,2847 @@ +[ + { + "type": "text", + "text": "DEPLOYMENT-EFFICIENT REINFORCEMENT LEARNING VIA MODEL-BASED OFFLINE OPTIMIZATION ", + "text_level": 1, + "bbox": [ + 176, + 99, + 826, + 146 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tatsuya Matsushima∗ Hiroki Furuta∗ Yutaka Matsuo The University of Tokyo {matsushima, furuta, matsuo}@weblab.t.u-tokyo.ac.jp ", + "bbox": [ + 184, + 169, + 686, + 212 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ofir Nachum ", + "text_level": 1, + "bbox": [ + 184, + 234, + 277, + 247 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shixiang Shane Gu ", + "text_level": 1, + "bbox": [ + 312, + 233, + 447, + 247 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Google Research ", + "bbox": [ + 186, + 248, + 297, + 261 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{ofirnachum, shanegu}@google.com ", + "bbox": [ + 186, + 262, + 498, + 275 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 313, + 544, + 327 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most reinforcement learning (RL) algorithms assume online access to the environment, in which one may readily interleave updates to the policy with experience collection using that policy. However, in many real-world applications such as health, education, dialogue agents, and robotics, the cost or potential risk of deploying a new data-collection policy is high, to the point that it can become prohibitive to update the data-collection policy more than a few times during learning. With this view, we propose a novel concept of deployment efficiency, measuring the number of distinct data-collection policies that are used during policy learning. We observe that naïvely applying existing model-free offline RL algorithms recursively does not lead to a practical deployment-efficient and sample-efficient algorithm. We propose a novel model-based algorithm, Behavior-Regularized Model-ENsemble (BREMEN), that not only performs better than or comparably as the state-of-the-art dynamic-programming-based and concurrently-proposed model-based offline approaches on existing benchmarks, but can also effectively optimize a policy offline using 10-20 times fewer data than prior works. Furthermore, the recursive application of BREMEN achieves impressive deployment efficiency while maintaining the same or better sample efficiency, learning successful policies from scratch on simulated robotic environments with only 5-10 deployments, compared to typical values of hundreds to millions in standard RL baselines. ", + "bbox": [ + 232, + 344, + 766, + 608 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 637, + 334, + 652 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reinforcement learning (RL) algorithms have recently demonstrated impressive success in learning behaviors for a variety of sequential decision-making tasks (Barth-Maron et al., 2018; Hessel et al., 2018; Nachum et al., 2019). Virtually all of these demonstrations have relied on highly-frequent online access to the environment, with the RL algorithms often interleaving each update to the policy with additional experience collection of that policy acting in the environment. However, in many real-world applications of RL, such as health (Murphy et al., 2001), education (Mandel et al., 2014), dialog agents (Jaques et al., 2019), and robotics (Gu et al., 2017a; Kalashnikov et al., 2018), the deployment of a new data-collection policy may be associated with a number of costs and risks. If we can learn tasks with a small number of data collection policies, we can substantially reduce them. ", + "bbox": [ + 174, + 670, + 825, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Based on this idea, we propose a novel measure of RL algorithm performance, namely deployment efficiency, which counts the number of changes in the data-collection policy during learning, as illustrated in Figure 1. This concept may be seen in contrast to sample efficiency or data efficiency (Precup et al., 2001; Degris et al., 2012; Gu et al., 2017b; Haarnoja et al., 2018; Lillicrap et al., 2016; Nachum et al., 2018), which measures the amount of environment interactions incurred during training, without regard to how many distinct policies were deployed to perform those interactions. Even when the data efficiency is high, the deployment efficiency could be low, since many on-policy and off-policy algorithms alternate data collection with each policy update (Schulman et al., 2015; Lillicrap et al., 2016; Gu et al., 2016; Haarnoja et al., 2018). Such dependence on high-frequency policy deployments is best illustrated in the recent works in offline RL (Fujimoto et al., 2019; Jaques et al., 2019; Kumar et al., 2019; Levine et al., 2020; Wu et al., 2019), where baseline off-policy algorithms exhibited poor performance when trained on a static dataset. These offline RL works, however, limit their study to a single deployment, which is enough for achieving high performance with data collected from a sub-optimal behavior policy, but often not from a random policy. In contrast to those prior works, we aim to learn successful policies from scratch in a manner that is both sample and deployment-efficient. ", + "bbox": [ + 174, + 801, + 823, + 885 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d4b7db2b7c0236b75d1498e37817a81892cf444ccaaf33effb12564d6ca2dc21.jpg", + "image_caption": [ + "Figure 1: Deployment efficiency is defined as the number of changes in the data-collection policy $( I )$ , which is vital for managing costs and risks of new policy deployment. Online RL algorithms typically require many iterations of policy deployment and data collection, which leads to extremely low deployment efficiency. In contrast, most pure offline algorithms consider updating a policy from a fixed dataset without additional deployment and often fail to learn from a randomly initialized data-collection policy. Interestingly, most state-of-the-art off-policy algorithms are still evaluated in heavily online settings. For example, SAC (Haarnoja et al., 2018) collects one sample per policy update, amounting to 100,000 to 1 million deployments for learning standard benchmark domains. " + ], + "image_footnote": [], + "bbox": [ + 212, + 99, + 794, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 422, + 825, + 549 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Many existing model-free offline RL algorithms (Levine et al., 2020) are tuned and evaluated on massive datasets (e.g., one million transitions). In order to develop an algorithm that is both sample and deployment-efficient, each iteration of the algorithm between successive deployments has to work effectively on much smaller dataset sizes. We believe model-based RL is better suited to this setting due to its higher demonstrated sample efficiency than model-free RL (Kurutach et al., 2018; Nagabandi et al., 2018). Although the combination of model-based RL and offline or limiteddeployment settings seems straight-forward, we find this naïve approach leads to poor performance. This problem can be attributed to extrapolation errors (Fujimoto et al., 2019) similar to those observed in model-free methods. Specifically, the learned policy may choose sequences of actions which lead it to regions of the state space where the dynamics model cannot predict properly, due to poor coverage of the dataset. This can lead the policy to exploit approximation errors of the dynamics model and be disastrous for learning. In model-free settings, similar data distribution shift problems are typically remedied by regularizing policy updates explicitly with a divergence from the observed data distribution (Jaques et al., 2019; Kumar et al., 2019; Wu et al., 2019), which, however, can overly limit policies’ expressivity (Sohn et al., 2020). ", + "bbox": [ + 174, + 556, + 825, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In order to better approach these problems arising in limited deployment settings, we propose Behavior-Regularized Model-ENsemble (BREMEN), which learns an ensemble of dynamics models in conjunction with a policy using imaginary rollouts while implicitly regularizing the learned policy via appropriate parameter initialization and conservative trust-region learning updates. We evaluate BREMEN on standard offline RL benchmarks of high-dimensional continuous control tasks, where only a single static dataset is used. In this fixed-batch setting, our experiments show that BREMEN can not only achieve performance competitive with state-of-the-art when using standard dataset sizes but also learn with 10-20 times smaller datasets, which previous methods are unable to attain. Enabled by such stable and sample-efficient offline learning, we show that BREMEN can learn successful policies with only 5-10 deployments in the online setting, significantly outperforming existing off-policy and offline RL algorithms in deployment efficiency while keeping sample efficiency. ", + "bbox": [ + 174, + 771, + 825, + 924 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 PRELIMINARIES ", + "text_level": 1, + "bbox": [ + 176, + 102, + 338, + 117 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We consider a Markov Decision Process (MDP) setting, characterized by the tuple $\\begin{array} { r l } { \\mathcal { M } } & { { } = } \\end{array}$ $( S , \\mathcal { A } , p , r , \\gamma )$ , where $s$ is the state space, $\\mathcal { A }$ is the action space, $p ( s ^ { \\prime } | s , a )$ is the transition probability distribution or dynamics, $r ( s )$ is the reward function and $\\gamma \\in ( 0 , 1 )$ is the discount factor. A policy $\\pi$ is a function that determines the agent behavior, mapping from states to probability distributions over actions. The goal is to obtain the optimal policy $\\pi ^ { * }$ , which maximizes the expectation of discounted sum of rewards. The transition probability $p ( s ^ { \\prime } | s , a )$ is usually unknown, and estimated with a parameterized dynamics model $f _ { \\phi }$ (e.g. a neural network) in model-based RL. For simplicity, we assume that the reward function $r ( s )$ is known, and the reward can be computed for any arbitrary state, but we may extend to the unknown setting and predict it using a parameterized function. ", + "bbox": [ + 174, + 133, + 825, + 260 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "On-policy vs Off-policy, Online vs Offline At a high-level, most RL algorithms alternate many times between collecting a batch of transitions (deployments) and optimizing the policy (learning). If the algorithms discard data after each policy update, they are on-policy (Schulman et al., 2015; 2017), while if they accumulate data in a buffer $\\mathcal { D }$ , i.e. experience replay (Lin, 1992), they are off-policy (Mnih et al., 2015; Lillicrap et al., 2016; Gu et al., 2016; 2017b; Haarnoja et al., 2018; Fujimoto et al., 2019; Fakoor et al., 2019) because not all the data in buffer comes from the current policy. However, we consider all these algorithms to be online RL algorithms, since they involve many deployments during learning, ranging from hundreds to millions. On the other hand, in pure offline RL, one does not assume direct interaction and learns a policy from only a fixed dataset, which effectively corresponds to a single deployment allowed for learning. Classically, interpolating these two extremes were semi-batch RL algorithms (Lange et al., 2012; Singh et al., 1995), which improve the policy through repetitions of collecting a large batch of transitions $\\mathcal { D } = \\{ ( s , a , s ^ { \\prime } , r ) \\}$ and performing many or full policy updates. While these semi-batch RL also realize good deployment efficiency, they have not been extensively studied with neural network function approximators or in off-policy settings with experience replay for scalable sample-efficient learning. In our work, we aim to have both high deployment efficiency and sample efficiency by developing an algorithm that can solve the tasks with minimal policy deployments as well as transition samples. ", + "bbox": [ + 174, + 266, + 825, + 502 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 DEPLOYMENT EFFICIENCY ", + "text_level": 1, + "bbox": [ + 178, + 523, + 428, + 540 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Deploying a new policy for data collection can be associated with a number of costs and risks for many real-world applications like medicine, dialogue systems, or robotic control (Murphy et al., 2001; Mandel et al., 2014; Gu et al., 2017a; Kalashnikov et al., 2018; Nachum et al., 2019; Jaques et al., 2019). While there are abundant works on safety for RL (Chow et al., 2015; Eysenbach et al., 2018; Chow et al., 2018; Ray et al., 2019; Chow et al., 2019), they often do not provide guarantees in practice when combined with neural networks and stochastic optimization. It is therefore necessary to verify each policy before deployment (e.g. measuring the variance of rewards or checking out-of-bounds actions). Due to such costs associated with each deployment, it is desirable to minimize the number of distinct deployments needed during the learning process. Even ignoring safety considerations, frequent updates to a deployed policy can exacerbate communication bottlenecks in large-scale distributed RL systems, which are becoming more prevalent (Nair et al., 2015; Espeholt et al., 2018; 2019). We additionally discuss on the importance of the deployment efficiency in real-world applications. See Appendix C. ", + "bbox": [ + 174, + 556, + 826, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to focus research on these practical bottlenecks, we propose a novel measure of RL algorithms, namely, deployment efficiency, which counts how many times the data-collection policy has been changed during improvement from random policy to solve the task. For example, if an RL algorithm operates by using its learned policy to collect transitions from the environment $I$ times, each time collecting a batch of $B$ new transitions, then the number of deployments is $I$ , while the total number of samples collected is $I \\times B$ . The lower $I$ is, the more deployment-efficient the algorithm is; in contrast, sample efficiency looks at $I \\times B$ . Online RL algorithms, whether they are on-policy or off-policy, typically update the policy and acquire new transitions by deploying the newly updated policy at every iteration. This corresponds to performing hundreds to millions of deployments during learning on standard benchmarks (Haarnoja et al., 2018), which is severely deployment inefficient. On the other hand, offline RL literature only studies the case of 1 deployment. A deployment-efficient algorithm would stand in the middle of these two extremes and ideally learn a successful policy from scratch while deploying only a few distinct policies, as illustrated in Figure 1. ", + "bbox": [ + 174, + 743, + 825, + 924 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recent deep RL literature seldom emphasizes deployment efficiency, with few exceptions in specific applications (Kalashnikov et al., 2018) where such a learning procedure is necessary. Deploymentinefficient algorithms will fail in scenarios where the deployment of each new policy is exorbitantly expensive, such as safety-critical robotics or user-facing products. Although current state-of-the-art algorithms on continuous control have substantially improved sample or data efficiency, they have not optimized for deployment efficiency. For example, SAC (Haarnoja et al., 2018), an efficient model-free off-policy algorithm, performs half a million to one million policy deployments during learning on MuJoCo (Todorov et al., 2012) benchmarks. ME-TRPO (Kurutach et al., 2018), a model-based algorithm, performs a much lower 100-300 policy deployments, although this is still relatively high for practical settings.2 In our work, we demonstrate successful learning on standard benchmark environments with only 5-10 deployments. ", + "bbox": [ + 174, + 103, + 825, + 256 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4 BEHAVIOR-REGULARIZED MODEL-ENSEMBLE ", + "text_level": 1, + "bbox": [ + 174, + 276, + 594, + 294 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve a favorable combination of both high deployment and sample efficiency, we propose Behavior-Regularized Model-ENsemble (BREMEN). BREMEN incorporates Dyna-style (Sutton, 1991; Kurutach et al., 2018) model-based RL, learning an ensemble of dynamics models in conjunction with a policy using imaginary rollouts and behavior regularization via conservative trust-region updates. ", + "bbox": [ + 174, + 309, + 826, + 380 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1 IMAGINARY ROLLOUT FROM MODEL ENSEMBLE ", + "text_level": 1, + "bbox": [ + 174, + 396, + 552, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As in recent Dyna-style model-based RL methods (Kurutach et al., 2018; Wang et al., 2019), BREMEN uses an ensemble of $K$ deterministic dynamics models $\\hat { f } _ { \\phi } = \\left\\{ \\hat { f } _ { \\phi _ { 1 } } , \\dots , \\hat { f } _ { \\phi _ { K } } \\right\\}$ to alleviate the problem of model bias. Each model $\\hat { f } _ { \\phi _ { i } }$ is parameterized by $\\phi _ { i }$ and trained by the following objective, which minimizes mean squared error between the prediction of next state $\\hat { f } _ { \\phi _ { i } } \\left( s _ { t } , a _ { t } \\right)$ and true next state $s _ { t + 1 }$ over a dataset $\\mathcal { D }$ : ", + "bbox": [ + 173, + 422, + 826, + 508 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/acece41c73ec2f834ca9cf9b6bd7fc9f42921e41dec46df584818bce145a09d4.jpg", + "text": "$$\n\\operatorname* { m i n } _ { \\phi _ { i } } \\frac { 1 } { | \\mathcal { D } | } \\sum _ { \\left( s _ { t } , a _ { t } , s _ { t + 1 } \\right) \\in \\mathcal { D } } \\frac { 1 } { 2 } \\left. s _ { t + 1 } - \\hat { f } _ { \\phi _ { i } } \\left( s _ { t } , a _ { t } \\right) \\right. _ { 2 } ^ { 2 } .\n$$", + "text_format": "latex", + "bbox": [ + 336, + 516, + 660, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During training of a policy $\\pi _ { \\theta }$ , imagined trajectories of states and actions are generated sequentially, using a dynamics model $\\hat { f } _ { \\phi _ { i } }$ that is randomly selected at each time step: ", + "bbox": [ + 169, + 563, + 825, + 594 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/dc95e3b3e4427eee9f1dd8c199b2f4aa7b26ef0533ddc221497d05deb5fd6650.jpg", + "text": "$$\na _ { t } \\sim \\pi _ { \\theta } ( \\cdot | \\hat { s } _ { t } ) , \\quad \\hat { s } _ { t + 1 } = \\hat { f } _ { \\phi _ { i } } ( \\hat { s } _ { t } , a _ { t } ) \\quad \\mathrm { w h e r e } \\quad i \\sim \\{ 1 \\cdot \\cdot \\cdot K \\} .\n$$", + "text_format": "latex", + "bbox": [ + 295, + 602, + 700, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2 POLICY UPDATE WITH BEHAVIOR REGULARIZATION ", + "text_level": 1, + "bbox": [ + 174, + 637, + 580, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to manage the discrepancy between the true dynamics and the learned model caused by the distribution shift in batch settings, we propose to use iterative policy updates via a trust-region constraint, re-initialized with a behavior-cloned policy after every deployment. Specifically, after each deployment, we are given an updated dataset of experience transitions $\\mathcal { D }$ . With this dataset, we approximate the true behavior policy $\\pi _ { b }$ through behavior cloning (BC), utilizing a neural network $\\hat { \\pi } _ { \\beta }$ parameterized by $\\beta$ , where we implicitly assume a fixed variance, a common practice in BC (Rajeswaran et al., 2017): ", + "bbox": [ + 173, + 664, + 825, + 762 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/28f2399f44d1d36e1e311585fa4505b5585f6ceb535df8d77fee6acdc89a6c43.jpg", + "text": "$$\n\\operatorname* { m i n } _ { \\beta } \\frac { 1 } { | \\mathscr { D } | } \\sum _ { ( s _ { t } , a _ { t } ) \\in \\mathscr { D } } \\frac { 1 } { 2 } \\left. a _ { t } - \\hat { \\pi } _ { \\beta } \\left( s _ { t } \\right) \\right. _ { 2 } ^ { 2 } .\n$$", + "text_format": "latex", + "bbox": [ + 372, + 768, + 624, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After obtaining the estimated behavior policy, we initialize the target policy $\\pi _ { \\theta }$ as a Gaussian policy with mean from $\\hat { \\pi } _ { \\beta }$ and standard deviation of 1. This BC initialization in conjunction with gradient descent based optimization may be seen as implicitly biasing the optimized $\\pi _ { \\theta }$ to be close to the data-collection policy (Nagarajan & Kolter, 2019), and thus works as a remedy for the distribution shift problem (Ross et al., 2011). To further bias the learned policy to be close to the data-collection ", + "bbox": [ + 174, + 815, + 825, + 886 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 BREMEN for Deployment-Efficient RL ", + "text_level": 1, + "bbox": [ + 174, + 103, + 500, + 118 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d3126046e5e54a3a6f42fe5bd2e6226e1b66a423e4c630c85402fa980d756fdb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Input: Empty dataset Dau,D,Initial parameters Φ = {1,·,Φk},β,Number of policy optimization T
Numberof deploymentsI.
1:Randomly initialize the target policy πθ .
2:for deploymenti=1,·.,I do
3:Collect B transitions in the true environment using T and add them to dataset
Dall←DalU{St,at,rt,St+1},D←{st,at,rt,St+1}.
4:Train K dynamics models f using Dau via Equation 1.
5: 6:Train estimated behavior policy πβ using D by behavior cloning via Equation 3.
7:Re-initialize target policy πeo = Normal(β,1). for policy optimization k =1,..·,T do
8:Generate imaginary rollout via Equation 2.
9:Optimize target policy Tβ satisfying Equation 4 with the rollout.
", + "bbox": [ + 176, + 122, + 823, + 281 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "policy, we opt to use a KL-based trust-region optimization (Schulman et al., 2015). Therefore, the optimization of BREMEN becomes ", + "bbox": [ + 173, + 309, + 823, + 337 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/8af682036a9c8970146000e325dfec08320cd1c07d20dafde4f6238f0d1bf694.jpg", + "text": "$$\n\\begin{array} { r l } & { \\theta _ { k + 1 } = \\underset { \\theta } { \\arg \\operatorname* { m a x } } \\ \\underset { s , a \\sim \\pi _ { \\theta _ { k } } , \\hat { f } _ { \\phi _ { i } } } { \\mathbb { E } } [ \\frac { \\pi _ { \\theta } ( a | s ) } { \\pi _ { \\theta _ { k } } ( a | s ) } A ^ { \\pi _ { \\theta _ { k } } } ( s , a ) ] } \\\\ & { \\mathrm { s . t . } \\quad \\underset { s \\sim \\pi _ { \\theta _ { k } } , \\hat { f } _ { \\phi _ { i } } } { \\mathbb { E } } [ D _ { \\mathrm { K L } } ( \\pi _ { \\theta } ( \\cdot | s ) | | \\pi _ { \\theta _ { k } } ( \\cdot | s ) ) ] \\leq \\delta , \\quad \\pi _ { \\theta _ { 0 } } = \\mathrm { N o r m a l } ( \\hat { \\pi } _ { \\beta } , 1 ) , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 248, + 344, + 746, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $A ^ { \\pi _ { \\theta _ { k } } } ( s , a )$ is the advantage of $\\pi _ { \\theta _ { k } }$ computed using model-based rollouts in the learned dynamics model and $\\delta$ is the maximum step size. ", + "bbox": [ + 174, + 420, + 823, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The combination of BC for initialization and finite iterative trust-region updates serves as an implicit KL regularization. This is in contrast to many previous offline RL algorithms that augment the value function with a penalty of explicit KL divergence (Siegel et al., 2020; Wu et al., 2019) or maximum mean discrepancy (Kumar et al., 2019). Empirically, we found that our regularization technique outperforms the explicit KL penalty (Section 5.3). Furthermore, we provide a mathematical intuition explaining how our methods works as an implicit regularization of distributional shift in Appendix A. ", + "bbox": [ + 174, + 455, + 825, + 540 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By recursively performing offline procedure, BREMEN can be used for deployment-efficient learning as shown in Algorithm 1, starting from a randomly initialized policy, collecting experience data, and performing offline policy updates. ", + "bbox": [ + 174, + 546, + 825, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5 EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 611, + 326, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to realize a deployment-efficient RL algorithm, the batch policy optimizer has to be stable and sample-efficient. We first evaluate BREMEN in the offline setting, where the algorithm learns the policy from a static dataset. Standard benchmarks of MuJoCo physics simulator shown in $\\mathrm { W u }$ et al., 2019) and more recent datasets (Fu et al., 2020) are used in the evaluation, and we compared the asymptotic performance of BREMEN with other offline RL methods including the concurrent model-based approaches. We then tested the sample-efficiency of offline algorithms using smaller datasets. We lastly extend the experiment to deployment-efficient settings, where the algorithms learn their policies from scratch via a limited number of deployments and perform some ablations to see how components in BREMEN affect performance. See Appendix F for further details. ", + "bbox": [ + 173, + 642, + 825, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1 EVALUATING OFFLINE RL PERFORMANCES ", + "text_level": 1, + "bbox": [ + 174, + 785, + 516, + 800 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Standard Benchmarks We evaluate BREMEN on standard offline RL benchmarks following and identical protocol as in Wu et al. (2019): We first train online SAC to a certain cumulative reward threshold, 4,000 in HalfCheetah, 1,000 in Ant, Hopper, and Walker2d, and collect offline datasets. We evaluate agents with the offline dataset of one million (1M) transitions, which is standard for BCQ and BRAC. Table 1 (top) shows that BREMEN can achieve performance competitive with state-of-the-art model-free offline RL algorithms when using the standard dataset size of 1M. We also test BREMEN with more recent benchmarks of D4RL (Fu et al., 2020) and compared the performance with the existing model-free and model-based methods. See Appendix D for the results. ", + "bbox": [ + 174, + 811, + 825, + 924 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/da843c61732773303b62a35fa53a00983025285105e1b4d41a644d386b72b9a6.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1: Comparison of BREMEN to the existing offline methods on static datasets. Each cell shows the average cumulative reward and their standard deviation, where the number of samples is 1M, 100K, and 50K, respectively. The maximum steps per episode is 1,000. BRAC applies a primal form of KL value penalty, and BRAC (max Q) means its variant of sampling multiple actions and taking the maximum according to the learned Q function. " + ], + "table_body": "
1,000,000(1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset BC1191 1321±141412611281376
4281±12 5783±2721341±161 1130±1271421±147 2153±753
BCQ2021±31 2072±2851422±90
BRAC7192±1152239±1124
BRAC (max Q)2369±2347320±911916±3432409±1210
BREMEN (Ours)3328±2758055±1032058±8522346±230
ME-TRPO (offline)1258±5501804±924518±91211±154
100,000(100K)transitions
MethodAntHalfCheetahHopperWalker2d
Dataset1191406611281376
BC1330±814266±211322±1091426±47
BCQ1363±1993915±4111129±2382187±196
BRAC-157±3832505±25011310±702162±1109
BRAC (max Q)-226±3872332±24221422±1012164±1114
BREMEN (Ours)1633±1276095±3702191±4552132±301
ME-TRPO (offline)974±42±434307±17010±61
50,000 (50K) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset1191413811281376
BC1270±654230±491249±611420±194
BCQ1329±951319±6261178±2351841±439
BRAC-878±244-597±731277±102976±1207
BRAC (max Q)-843±279-590±561276±225903±1137
BREMEN(Ours)1347±2835823±1461632±7962280±647
938±32
ME-TRPO (offfline)-73±95152±13176±343
", + "bbox": [ + 250, + 103, + 746, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluating Sample-Efficiency We then evaluate the sample-efficiency by making much smaller datasets of $5 0 \\mathrm { k }$ and $1 0 0 \\mathrm { k }$ transitions $5 \\sim 1 0 \\%$ of Wu et al. (2019)). Surprisingly, Table 1 (middle and bottom) shows that BREMEN can also learn with smaller datasets, where BCQ and BRAC are unable to exceed even BC baseline. This is a novel evaluation protocol we proposed, and our BREMEN’s superior performance here is exactly what enables recursive BREMEN in the next section to be an effective algorithm in deployment-constrained settings. ", + "bbox": [ + 174, + 534, + 825, + 617 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2 EVALUATING DEPLOYMENT EFFICIENCY IN ONLINE RL BENCHMARKS ", + "text_level": 1, + "bbox": [ + 174, + 635, + 705, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare BREMEN to ME-TRPO, SAC, BCQ, and BRAC applied to limited deployment settings. To adapt offline methods (BCQ, BRAC) to this setting, we simply apply them in a recursive fashion;3 at each deployment iteration, we collect a batch of data with the most recent policy and then run the offline update with this dataset. As for SAC, we simply change the replay buffer to update only at specific deployment intervals. For the sake of comparison, we align the number of deployments and the amount of data collection at each deployment (either $1 0 0 \\mathrm { k }$ or $2 0 0 \\mathrm { k }$ ) for all methods.4 ", + "bbox": [ + 174, + 661, + 825, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 2 shows the results with $2 0 0 \\mathrm { k }$ (top) and $1 0 0 \\mathrm { k }$ (bottom) batched transitions per deployment. Regardless of the environments and the batch size per update, BREMEN achieves remarkable performance while existing online and offline RL methods struggle to make any progress. As a point of comparison, we also include results for online SAC and ME-TRPO without deployment-limits but using the same number of transitions. We additionally compare BREMEN to the model-based offline RL methods with uncertainty-based penalties. See Appendix E for further details. ", + "bbox": [ + 174, + 752, + 825, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following the motivation of deployment efficiency, obtaining a successful policy under data-collection constraint conditions in the real application, we extensively evaluate our algorithm on more realistic robotics environments in OpenAI Gym. The experimental procedure is the same as above, while we limit the batch size at each deployment as only $2 5 \\mathrm { k }$ . Figure 3 presents the reaching tasks with Fetch robot and 20-DoF shadow hand (Plappert et al., 2018), and the experimental results in both environments. Only BREMEN shows stable improvement and high performance, while other offline and online algorithms fail to learn. These results suggest that a model-based method is a desirable approach for satisfying practical requirements in robotics, i.e. sample and deployment efficiency. ", + "bbox": [ + 176, + 843, + 823, + 886 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6a1cb8fc593fa991de860c81499864a36dc243a21b814426030744b691e27217.jpg", + "image_caption": [ + "Figure 2: Evaluation of BREMEN with the existing methods (ME-TRPO, SAC, BCQ, BRAC) under deployment constraints (to 5-10 deployments with batch sizes of 200k and 100k). The average cumulative rewards and their standard deviations with 5 random seeds are shown. Vertical dotted lines represent where each policy deployment and data collection happen. BREMEN is able to learn successful policies with only 5-10 deployments, while the state-of-the-art off-policy (SAC), model-based (ME-TRPO), and recursively-applied offline RL algorithms (BCQ, BRAC) often struggle to make any progress. For completeness, we show ME-TRPO(online) and SAC(online) which are their original optimal learning curves without deployment constraints, plotted with respect to samples normalized by the batch size. While SAC(online) substantially outperforms BREMEN in sample efficiency, it uses 1 deployment per sample, leading to 100k-500k deployments required for learning. Interestingly, BREMEN achieves even better performance than the original ME-TRPO(online), suggesting the effectiveness of implicit behavior regularization. For SAC and ME-TRPO under deployment-constrained evaluation, their batch size between policy deployments differs substantially from their standard settings, and therefore we performed extensive hyper-parameter search on the relevant parameters such as the number of policy updates between deployments, as discussed in Appendix F.2.1. " + ], + "image_footnote": [], + "bbox": [ + 196, + 102, + 805, + 263 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/aefe5703a6af1bb98f484da513d1f7861b5ff52440d53d4cfceab98875c791d8.jpg", + "image_caption": [ + "Figure 3: Robotics environments and the results under deployment constraints (10 deployments with batch sizes of 25k). The performances are averaged over 5 seeds. BREMEN seems the only method that shows both stable improvement and solving tasks without large degradation or sub-optimal convergence. " + ], + "image_footnote": [], + "bbox": [ + 212, + 484, + 776, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 669, + 825, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3 ABLATION: EVALUATING EFFECTIVENESS OF IMPLICIT KL CONTROL ", + "text_level": 1, + "bbox": [ + 176, + 757, + 696, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we present an experiment to better understand the effect of BREMEN’s implicit regularization. Figure 4 shows the KL divergence of learned policies from the last deployed policy. We compare BREMEN to variants of BREMEN that use an explicit KL penalty on value instead of BC initialization (conservative KL trust-region updates are still used). We find that the explicit KL without behavior initialization variants learn policies that move farther away from the last deployed policy than behavior initialized policies. This suggests that the implicit behavior regularization employed by BREMEN is more effective as a conservative policy learning protocol. In addition, to assess the effect of repeated behavior cloning initialization, we also evaluate a variant of BREMEN without behavior cloning re-initialization (grey). This variant works in easier environments (Ant, Halfcheetah), but does not show remarkable progress in more challenging ones with termination (Hopper, Walker2d). ", + "bbox": [ + 174, + 785, + 825, + 924 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/caaaeaae5c063a15f89b51e7364e62582bf4f0db0e551d24fb5de280da818a2c.jpg", + "image_caption": [ + "Figure 4: We examine average cumulative rewards (top) and corresponding KL divergence between the last deployed policy and the target policy (bottom) with batch size 200K in limited deployment settings. The behavior initialized policy remains close to the last deployed policy during improvement without explicit value penalty $- \\alpha D _ { \\mathrm { K L } } ( { \\bar { \\pi _ { \\theta } } } \\| { \\hat { \\pi } } _ { \\beta } )$ . The explicit penalty is controlled by a coefficient $\\alpha$ . " + ], + "image_footnote": [], + "bbox": [ + 191, + 101, + 810, + 282 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This result empirically supports the need for repeated behavior initialization after each deployment. \nThe results of further experiments are shown in Appendix G. ", + "bbox": [ + 174, + 364, + 823, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6 RELATED WORK ", + "text_level": 1, + "bbox": [ + 176, + 414, + 344, + 429 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Deployment Efficiency and Offline RL Although we are not aware of any previous works which explicitly proposed the concept of deployment efficiency, its necessity in many real-world applications has been generally known. One may consider previously proposed semi-batch RL algorithms (Ernst et al., 2005; Lange et al., 2012; Singh et al., 1994; Roux, 2016) or theoretical analysis of switching cost under the tabular PAC-MDP settings (Bai et al., 2019; Guo & Brunskill, 2015) as approaching this issue. More recently, a related but distinct problem known as offline RL has gained popularity (Levine et al., 2020; Wu et al., 2019; Agarwal et al., 2019; Kumar et al., 2020). These works consider an extreme version of 1 deployment, and typically collect the static batch with a partially trained policy rather than a random policy. While offline RL has shown promising results for a variety of real-world applications, such as robotics (Mandlekar et al., 2019), dialogue systems (Jaques et al., 2019), or medical treatments (Gottesman et al., 2018), these algorithms struggle when learning a policy from scratch or when the dataset is small. Nevertheless, common themes of many offline RL algorithms – regularizing the learned policy to the behavior policy (Fujimoto et al., 2019; Kumar et al., 2019; Siegel et al., 2020; Wu et al., 2019) and utilizing ensembles to handle uncertainty (Kumar et al., 2019; Wu et al., 2019) – served as inspirations for the proposed our algorithm. A major difference of BREMEN from prior works is that the target policy is not explicitly forced to stick close to the estimated behavior policy through the policy update except for the initial iteration. Rather, BREMEN employs a more implicit regularization by initializing the learned policy with a behavior cloned policy and then applying conservative trust-region updates. Another major difference is the application of model-based approaches to fully offline settings, which has not been extensively studied in prior works (Levine et al., 2020), except the two concurrent works (Kidambi et al., 2020; Yu et al., 2020) that study pessimistic or uncertainty penalized MDPs with guarantees – closely related to Liu et al. (2019). By contrast, our work shows that a simple technique can already enable model-based offline algorithms to significantly outperform the prior model-free methods, and is, to the best of our knowledge, the first to define and extensively evaluate deployment efficiency with recursive experiments. ", + "bbox": [ + 173, + 445, + 825, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Model-Based RL There are many types of model-based RL algorithms (Sutton, 1991; Deisenroth & Rasmussen, 2011; Heess et al., 2015). A simple algorithmic choice is Dyna-style (Sutton, 1991), which uses a parameterized model to estimate the true MDP transition function, stochastically mapping states and actions to next states. The dynamics model can then serve as a simulator of the environment during policy updates. Dyna-style algorithms often suffer from the distributional shift, also known as model bias, which leads RL agents to exploit regions where the data is insufficient, and significant performance degradation. A variety of remedies have been proposed to relieve the issue of model bias, such as the use of multiple dynamics models as an ensemble (Chua et al., 2018; Kurutach et al., 2018; Janner et al., 2019), meta-learning (Clavera et al., 2018), energy-based regularizer (Boney et al., 2019), game-theoretic framework (Rajeswaran et al., 2020), and explicit penalty for unknown states (Kidambi et al., 2020; Yu et al., 2020). Notably, we have employed a subset of these remedies – model ensembles and trust-region updates (Kurutach et al., 2018) – for BREMEN. Compared to prior works, our work is notable for using BC initialization in conjunction with trust-region updates to alleviate the distribution shift of the learned policy from the dataset used to train the dynamics model. ", + "bbox": [ + 174, + 811, + 825, + 924 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 825, + 188 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7 CONCLUSION ", + "text_level": 1, + "bbox": [ + 176, + 208, + 318, + 223 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work, we introduced deployment efficiency, a novel measure for RL performance that counts the number of changes in the data-collection policy during learning. To enhance deployment efficiency, we proposed a novel model-based offline algorithm, Behavior-Regularized Model-ENsemble (BREMEN), combining model-ensembles with trust region updates from model-based RL literature (Kurutach et al., 2018), and policy initialization with behavior cloning from offline RL literature (Fujimoto et al., 2019; Wu et al., 2019). Crucially, BREMEN can improve policies offline sample-efficiently even when the batch size is 10-20 times smaller than prior works, allowing BREMEN to achieve impressive results in limited deployment settings, obtaining successful policies from scratch in only 5-10 deployments. Not only can this help alleviate costs and risks in real-world applications, but it can also reduce the amount of communication required during distributed learning and could form the basis for communication-efficient large-scale RL in contrast to prior works (Nair et al., 2015; Espeholt et al., 2018; 2019). Most critically, we show that under deployment efficiency constraints, most prior algorithms – model-free or model-based, online or offline – fail to achieve successful learning. One possible direction for future work is to incorporate verification efficiency into consideration, since a stochastic multi-modal policy could collect more diverse transitions while it takes more trajectories to be verified for safety than a uni-modal policy. While we presented promising results on some realistic simulated environments, validating BREMEN on real robots is another direction. We hope our work can gear the research community to value deployment efficiency as an important criterion for RL algorithms, and to eventually achieve similar sample efficiency and asymptotic performance as the state-of-the-art algorithms like SAC (Haarnoja et al., 2018) while having the deployment efficiency well-suited for safe and practical real-world reinforcement learning. 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", + "bbox": [ + 176, + 881, + 825, + 922 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "APPENDIX ", + "text_level": 1, + "bbox": [ + 176, + 102, + 263, + 118 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "A IMPLICIT KL CONTROL FROM A MATHEMATICAL PERSPECTIVE ", + "text_level": 1, + "bbox": [ + 174, + 133, + 740, + 152 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "We can intuitively understand that behavior cloning initialization with trust-region updates works as a regularization of distributional shift, and this can be supported by theory. Following the notation of Janner et al. (2019), we denote the generalization error of a dynamics model on the state distribution under the true behavior policy as $\\begin{array} { r } { \\epsilon _ { m } = \\operatorname* { m a x } _ { t } \\mathbb { E } _ { s \\sim d _ { t } ^ { \\pi _ { b } } } D _ { T V } ( \\bar { p ( } s _ { t + 1 } | s _ { t } , a _ { t } ) | | p _ { \\phi } ( s _ { t + 1 } | s _ { t } , a _ { t } ) ) } \\end{array}$ , where $D _ { T V }$ represents the total variation distance between true dynamics $p$ and learned model $p _ { \\phi }$ . We also denote the distribution shift on the target policy as $\\begin{array} { r } { \\operatorname* { m a x } _ { s } D _ { T V } ( \\pi _ { b } | | \\pi ) \\le \\epsilon _ { \\pi } } \\end{array}$ . A bound relating the true returns $\\eta [ \\pi ]$ and the model returns $\\hat { \\eta } [ \\pi ]$ on the target policy is given in Janner et al. (2019) as, ", + "bbox": [ + 173, + 165, + 825, + 267 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/d61ef7ba6dbba742a282990d7b12e361b9ee354446876eed6f9a57f566e8039b.jpg", + "text": "$$\n\\eta [ \\pi ] \\ge \\hat { \\eta } [ \\pi ] - \\left[ \\frac { 2 \\gamma r _ { m a x } ( \\epsilon _ { m } + 2 \\epsilon _ { \\pi } ) } { ( 1 - \\gamma ) ^ { 2 } } + \\frac { 4 r _ { m a x } \\epsilon _ { \\pi } } { ( 1 - \\gamma ) } \\right] .\n$$", + "text_format": "latex", + "bbox": [ + 330, + 271, + 666, + 306 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "This bound guarantees the improvement under the true returns as long as the improvement under the model returns increases by more than the slack in the bound due to $\\epsilon _ { m } , \\epsilon _ { \\pi }$ (Janner et al., 2019; Levine et al., 2020). ", + "bbox": [ + 174, + 309, + 825, + 352 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "We may relate this bound to the specific learning employed by BREMEN, which includes dynamics model learning, behavior cloning policy initialization, and conservative KL-based trust-region policy updates. To do so, we consider an idealized version of BREMEN, where the expectations over states in equations Equation 1, 3, 4 are replaced with supremums and the dynamics model is set to have unit variance. ", + "bbox": [ + 173, + 357, + 825, + 428 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Proposition 1 (Policy and model error bound). Suppose we apply the idealized BREMEN on a dataset $\\mathcal { D }$ , and define $\\epsilon _ { \\beta } , \\epsilon _ { \\phi }$ in terms of the behavior cloning and dynamics model losses as, ", + "bbox": [ + 171, + 431, + 823, + 460 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/c2f2c3d72e588942d1f90e27679108d3e13e651aa575885e47b8e07354fb2315.jpg", + "text": "$$\n\\begin{array} { r l } & { \\epsilon _ { \\beta } : = \\underset { s } { \\operatorname* { s u p } } \\mathbb { E } _ { a \\sim \\mathcal { D } ( - | s ) } [ \\| a - \\hat { \\pi } _ { \\beta } \\left( s \\right) \\| _ { 2 } ^ { 2 } / 2 ] - \\mathcal { H } ( \\pi _ { b } ( - | s ) ) } \\\\ & { \\epsilon _ { \\phi } : = \\underset { s , a } { \\operatorname* { s u p } } \\mathbb { E } _ { s ^ { \\prime } \\sim \\mathcal { D } ( - | s , a ) } \\left[ \\| s ^ { \\prime } - \\hat { f } _ { \\phi } ( s , a ) \\| _ { 2 } ^ { 2 } / 2 \\right] - \\mathcal { H } ( p ( - | s , a ) ) , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 292, + 465, + 705, + 525 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "where $\\mathcal { H }$ denotes the Shannon entropy. If one then applies $T$ KL-based trust-region steps of step size $\\delta$ (Equation 4) using stochastic dynamics models with mean $\\hat { f } _ { \\phi }$ and standard deviation $^ { l }$ , then ", + "bbox": [ + 169, + 529, + 825, + 560 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/8ccdfa3eb115b464fecd2fe3267fdfdd209a81219d9b0a18cf587294a3b2cc52.jpg", + "text": "$$\n\\epsilon _ { \\pi } = \\sqrt { \\frac { 1 } { 2 } \\epsilon _ { \\beta } + \\frac { d _ { a } } { 4 } \\log 2 \\pi } + T \\sqrt { \\frac { 1 } { 2 } \\delta } ; \\epsilon _ { m } \\leq \\sqrt { \\frac { 1 } { 2 } \\epsilon _ { \\phi } + \\frac { d _ { s } } { 4 } \\log 2 \\pi } ,\n$$", + "text_format": "latex", + "bbox": [ + 281, + 564, + 715, + 601 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "where $d _ { a }$ and $d _ { s }$ denotes the dimension of action and state space. ", + "bbox": [ + 174, + 604, + 602, + 619 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Proof. We first consider $\\epsilon _ { \\pi }$ . The behavior cloning objective in its supremum form is, ", + "bbox": [ + 176, + 633, + 728, + 648 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/510a7a6f4c53ed1fd9bf08aa7d02a389c968aa539179d59d749e976e7870b259.jpg", + "text": "$$\n\\begin{array} { r c l } { { \\epsilon _ { \\beta } } } & { { = } } & { { \\displaystyle \\operatorname* { s u p } _ { s \\in \\mathcal { D } } \\mathbb { E } _ { a \\sim \\mathcal { D } ( - | s ) } [ \\| a - \\hat { \\pi } _ { \\beta } \\left( s \\right) \\| _ { 2 } ^ { 2 } / 2 ] - \\mathcal { H } ( \\pi _ { b } ( - | s ) ) } } \\\\ { { } } & { { } } & { { \\displaystyle = } } & { { \\displaystyle \\operatorname* { s u p } _ { s \\in \\mathcal { D } } \\mathbb { E } _ { a \\sim \\mathcal { D } ( - | s ) } \\left[ - \\log \\pi _ { \\theta _ { 0 } } ( a | s ) \\right] - \\mathcal { H } ( \\pi _ { b } ( - | s ) ) - \\frac { d _ { a } } { 2 } \\log 2 \\pi } } \\\\ { { } } & { { } } & { { \\displaystyle = } } & { { \\displaystyle \\operatorname* { s u p } _ { s \\in \\mathcal { D } } D _ { K L } ( \\pi _ { b } ( - | s ) | | \\pi _ { \\theta _ { 0 } } ( - | s ) ) - \\frac { d _ { a } } { 2 } \\log 2 \\pi . } } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 269, + 652, + 727, + 752 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "We apply Pinsker’s inequality to the true and estimated behavior policy to yield ", + "bbox": [ + 173, + 755, + 692, + 770 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/cd03e1a355c462e8c51673a94646e5c30e546ca5516d39be57268f3f2d32018e.jpg", + "text": "$$\n\\operatorname* { s u p } _ { s } D _ { T V } ( \\pi _ { b } ( - | s ) | | \\pi _ { \\theta _ { 0 } } ( - | s ) ) \\leq { \\sqrt { { \\frac { 1 } { 2 } } \\epsilon _ { \\beta } + { \\frac { d _ { a } } { 4 } } \\log 2 \\pi } } .\n$$", + "text_format": "latex", + "bbox": [ + 320, + 773, + 676, + 810 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "By the same Pinsker’s inequality, we have, ", + "bbox": [ + 174, + 821, + 455, + 837 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/cc6a736a77029996a3131bc442a1cd7ba489b5215b67cb069131c1f6b0992f95.jpg", + "text": "$$\n\\operatorname* { s u p } _ { s } D _ { T V } \\big ( \\pi _ { \\theta _ { k } } ( - | s ) | | \\pi _ { \\theta _ { k + 1 } } ( - | s ) \\big ) \\leq \\sqrt { \\delta / 2 } .\n$$", + "text_format": "latex", + "bbox": [ + 354, + 840, + 642, + 869 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Therefore, by triangle inequality, we have ", + "bbox": [ + 174, + 872, + 449, + 887 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/adbda65b070ce562bc17233c93098a26063b412526439385966fa8c83b1bd933.jpg", + "text": "$$\n\\operatorname* { s u p } _ { s } D _ { T V } ( \\pi _ { b } ( - | s ) | | \\pi _ { \\theta _ { T } } ( - | s ) ) \\leq \\sqrt { \\frac { 1 } { 2 } \\epsilon _ { \\beta } + \\frac { d _ { a } } { 4 } \\log { 2 \\pi } } + T \\sqrt { \\frac { 1 } { 2 } \\delta } = \\epsilon _ { \\pi } ,\n$$", + "text_format": "latex", + "bbox": [ + 266, + 892, + 728, + 928 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "as desired. ", + "bbox": [ + 173, + 103, + 245, + 117 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "We perform similarly for $\\epsilon _ { m }$ . The model dynamics loss is ", + "bbox": [ + 173, + 125, + 553, + 140 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/aa87fc6f3057155c6737ed593a8a5dafd8d078ffdb95066df40607dddf37e869.jpg", + "text": "$$\n\\begin{array} { r c l } { { \\epsilon _ { \\phi } } } & { { = } } & { { \\displaystyle \\operatorname* { s u p } _ { s , a } \\mathbb { E } _ { s ^ { \\prime } \\sim \\mathcal { D } ( - | s , a ) } \\left[ \\| s ^ { \\prime } - \\hat { f } _ { \\phi } ( s , a ) \\| _ { 2 } ^ { 2 } / 2 \\right] - \\mathcal { H } ( p ( - | s , a ) ) } } \\\\ { { } } & { { } } & { { } } \\\\ { { \\displaystyle = } } & { { \\displaystyle \\operatorname* { s u p } _ { s , a } \\mathbb { E } _ { s ^ { \\prime } \\sim \\mathcal { D } ( - | s , a ) } \\left[ - \\log p _ { \\phi } ( s ^ { \\prime } | s , a ) \\right] - \\mathcal { H } ( p ( - | s , a ) ) - \\frac { d _ { s } } { 2 } \\log 2 \\pi } } \\\\ { { } } & { { } } & { { } } \\\\ { { \\displaystyle = } } & { { \\displaystyle \\operatorname* { s u p } _ { s , a } D _ { K L } ( p ( - | s , a ) | | p _ { \\phi } ( - | s , a ) ) - \\frac { d _ { s } } { 2 } \\log 2 \\pi . } } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 251, + 145, + 743, + 250 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "We apply Pinsker’s inequality to the true dynamics and learned model to yield ", + "bbox": [ + 171, + 253, + 687, + 270 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/dc340071f12361b39a5e91cdb583922019af7ff05d0a8d67d4402eec2d3f9721.jpg", + "text": "$$\n\\epsilon _ { m } \\leq \\operatorname* { s u p } _ { s , a } D _ { T V } ( p ( - | s , a ) | | p _ { \\phi } ( - | s , a ) ) \\leq \\sqrt { \\frac { 1 } { 2 } \\epsilon _ { \\phi } + \\frac { d _ { s } } { 4 } \\log 2 \\pi } ,\n$$", + "text_format": "latex", + "bbox": [ + 292, + 275, + 704, + 313 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "as desired. ", + "bbox": [ + 173, + 319, + 245, + 334 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "B TRADE-OFF BETWEEN SAMPLE AND DEPLOYMENT EFFICIENCY ", + "text_level": 1, + "bbox": [ + 174, + 353, + 736, + 371 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "An important aspect of deployment efficiency is the trade-off between sample and deployment efficiency. To collect multiple data points per experiment and show this trade-off, we run recursive BREMEN with different batch sizes, and record how many samples are required to cross different reward thresholds. ", + "bbox": [ + 173, + 385, + 825, + 441 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "HalfCheetah (Reward 7,000 result) and other results from Figure 5 generally show that high deployment efficiency lowers sample efficiency, confirming the inherent trade-off. However, in rare cases, e.g. Ant (Reward 5,000 result), it could be possible to achieve both high deployment efficiency and high sample efficiency through the right choice of the batch size hyper-parameter. ", + "bbox": [ + 173, + 449, + 826, + 506 + ], + "page_idx": 14 + }, + { + "type": "image", + "img_path": "images/e4a79595f8df889828b941ec6d05aca10bd9f4d0a7a9a704b384c7c841649438.jpg", + "image_caption": [ + "Figure 5: From the view of both sample and deployment efficiency at certain cumulative reward threshold, we evaluate BREMEN in Ant (left) and HalfCheetah (right). x and y axes respectively represent the number of samples and the number of deployments.Each data point comes from running BREMEN with different reward thresholds and batch sizes. The numbers above the points (e.g. 1000, 2000, ...) represent the reward threshold. The results (especially, reward 7,000 threshold in HalfCheetah) generally show that high deployment efficiency lowers sample efficiency, confirming the inherent trade-off. " + ], + "image_footnote": [], + "bbox": [ + 207, + 520, + 789, + 660 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "C DISCUSSION: IMPORTANCE OF DEPLOYMENT EFFICIENCY IN REAL-WORLD APPLICATIONS ", + "text_level": 1, + "bbox": [ + 173, + 102, + 714, + 136 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Our notion of deployment-efficiency is necessitated by cost and safety constraints typical in many real world scenarios. Namely, a common approach to real-world applications (Cabi et al., 2020; DulacArnold et al., 2019; Kalashnikov et al., 2018) is the following iterative training and data-collection paradigm: ", + "bbox": [ + 174, + 151, + 826, + 207 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "1. Aggregate past previous dataset from worker(s) \n2. Update policy based on the collected data \n3. Deploy the policy to the worker(s) \n4. Monitor the policy works as expected e.g. checking if it does not violate safety criterion \n(this safety verification step may alternatively happen before step 3) \n5. Let the worker(s) collect experiences with the latest policy. ", + "bbox": [ + 210, + 219, + 825, + 324 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "It is easy to see that the number of deployments is a critical bottleneck, as it involves both monitoring of the policy (Step 4) and communication to the workers (Step 3), and both of these steps can incur significant cost. Specifically, Step 4 requires evaluating the policy for safety, and often requires human monitors (Atkeson et al., 2015). As for Step 3, communication to workers can also be a bottleneck, especially in highly-parallelized distributed RL systems (Nair et al., 2015; Espeholt et al., 2018; 2019). Every policy deployment requires a potentially expensive communication between different machines/processes, and this can be a bottleneck on the whole system. ", + "bbox": [ + 174, + 335, + 825, + 433 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "As a concrete example of the necessity of good deployment efficiency, consider optimization of personalization in web apps or recommender systems (Abel et al., 2017). Once a policy is learned on a batch of past experiences, it is deployed to a collection of web-hosting servers. In this scenario, both safety and communication concerns are relevant: Safety of the new policy is typically ensured by initially deploying the policy to a small percentage of users; after monitoring the results for some length of time (e.g. the newly deployed policy does not deteriorate user experiences), one can expand the target user set. As for communication, deploying a new policy to web-hosting servers can be time intensive, especially in large-scale web applications where the policy must be deployed to a network of servers around the world. Thus, in this setting, it is clear that online updating of the policy is infeasible due to both safety and communication constraints. Accordingly, the deployment-efficiency of any candidate RL algorithm is of tantamount importance. ", + "bbox": [ + 174, + 439, + 825, + 592 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "The safe exploration might be mentioned as a potential alternative to deployment-efficiency. While safe exploration can arguably tackle the first concern above (safety risks of the policy), it does nothing to mitigate the latter (the engineering or communication costs associated with online deployment of a policy). Furthermore, this still ignores the fact that in many scenarios the ability to do safe exploration is not a given. While some safe RL algorithms can provide guarantees in tabular cases, these guarantees no longer hold when using function approximation with neural networks (Chow et al., 2018). In these cases, it can be much more difficult to perform “safe exploration” than it is to develop a deployment-efficient algorithm. ", + "bbox": [ + 174, + 598, + 825, + 710 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "D EVALUATING OFFLINE PERFORMANCES ON D4RL DATASETS ", + "text_level": 1, + "bbox": [ + 173, + 102, + 717, + 118 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "We compare BREMEN to MOPO (Yu et al., 2020), concurrently proposed model-based offline methods penalized by model epistemic uncertainty, and state-of-the-art model-free offline algorithms, namely, CQL (Kumar et al., 2020), BEAR (Kumar et al., 2019), BRAC (Wu et al., 2019), AWR (Peng et al., 2019) and BCQ (Fujimoto et al., 2019), on the D4RL MuJoCo locomotion datasets (Fu et al., 2020), used as standard offline RL benchmarks (Kumar et al., 2020; Nair et al., 2020). They have several types of offline data collected with different strategies. We choose the hyper parameters of BREMEN in Section 5.1 and F.2.2. Table 2 shows BREMEN beats recent state-of-the-art algorithms with the highest normalized score (around 100 corresponds to an expert) in several tasks, while none of the methods consistently achieves the best performance. This result suggests that the implicit regularization with the model-based method performs surprisingly well in offline settings despite of its simplicity. ", + "bbox": [ + 173, + 133, + 825, + 286 + ], + "page_idx": 16 + }, + { + "type": "table", + "img_path": "images/31dde696c0594367a80d70f9fc4587080fb5a3e4444ebb5e37b594bb636d18eb.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2: Evaluation on D4RL MuJoCo locomotion datasets. The normalized score of BREMEN are averaged over 4 random seeds. We refer the score of MOPO (Yu et al., 2020) and CQL (Kumar et al., 2020) from their original papers. Other results are cited from Fu et al. (2020). BREMEN achieves the best and competitive score in several domains, while none of the algorithms beats all other methods. " + ], + "table_body": "
Task NameBCBREMENMOPOCQLBEARBRAC-vAWRBCQ
halfcheetah-randomwalker2d-randomhopper-random2.11.69.836.93.712.231.913.013.335.47.025.17.311.431.21.912.22.51.510.22.24.910.6
10.8
halfcheetah-mediumwalker2d-mediumhopper-medium36.16.629.055.059.669.340.214.026.544.479.258.041.759.152.146.381.131.137.417.435.940.753.154.5
halfcheetah-medium-replaywalker2d-medium-replayhopper-medium-replay38.411.311.847.27.624.154.042.792.546.238.619.233.747.70.90.640.315.528.438.2
26.748.615.033.1
halfcheetah-medium-expertwalker2d-medium-experthopper-medium-expert35.86.4111.953.355.264.657.955.051.762.498.7111.053.440.196.341.981.60.852.753.827.164.757.5110.9
", + "bbox": [ + 173, + 299, + 854, + 469 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "E INCORPORATING PESSIMISTIC MODEL-BASED OFFLINE METHODS INTO BREMEN ", + "text_level": 1, + "bbox": [ + 176, + 554, + 803, + 588 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "The concurrent model-based offline RL methods prescribe the use of uncertainty-based penalties (Kidambi et al., 2020; Yu et al., 2020), which can be incorporated into BREMEN. We therefore augmented BREMEN with either a hard (MOReL-like, green) or soft (MOPO-like, orange) reward penalty according to model uncertainty. MOReL quantifies the uncertainty measuring the maximum discrepancy of the prediction across the ensembles of the models and receives constant negative reward (-5.0 in our experiments) if the discrepancy is larger than the threshold (we set 3.0). MOPO measures the uncertainty by the maximum standard deviation of the model ensembles and uses this as a reward penalty with a coefficient (0.1 in our experiments). Evaluations in Figure 6 reveal that the soft reward penalty has notable results in Hopper and Walker2d, where model uncertainty is more crucial due to the episode’s termination. Hard reward penalty seems overly pessimistic in deployment-efficient settings. ", + "bbox": [ + 173, + 603, + 825, + 757 + ], + "page_idx": 16 + }, + { + "type": "image", + "img_path": "images/b92db87a8488301afcc0d533a6528c154563a870085080d2776b335a16c289e9.jpg", + "image_caption": [ + "Figure 6: Comparison to the pessimistic reward shaping incorporated into BREMEN. Soft reward penalty (MOPO-like, orange) performs well in the environments where the incomplete models appear to be fatal. " + ], + "image_footnote": [], + "bbox": [ + 186, + 772, + 813, + 867 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "F DETAILS OF EXPERIMENTAL SETTINGS ", + "text_level": 1, + "bbox": [ + 174, + 102, + 532, + 118 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "F.1 IMPLEMENTATION DETAILS ", + "text_level": 1, + "bbox": [ + 176, + 133, + 405, + 147 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "For our baseline methods, we use the open-source implementations of SAC, BC, BCQ, and BRAC published in Wu et al. (2019). SAC and BRAC have (300, 300) Q-Network and (200, 200) policy network. BC has (200, 200) policy network, and BCQ has (300, 300) Q-Network, (300, 300) policy network, and (750, 750) conditional VAE. As for online ME-TRPO, we utilize the codebase of model-based RL benchmark (Wang et al., 2019). BREMEN and online ME-TRPO use the policy consisting of two hidden layers with 200 units. The dynamics model also consists of two hidden layers with 1,024 units. We use Adam (Kingma & Ba, 2014) as the optimizer with the learning rate of 0.001 for the dynamics model, and 0.0005 for behavior cloning in BREMEN. Especially in BREMEN and online ME-TRPO, we adopt a linear feature value function to stabilize the training. BREMEN in deployment-efficient settings takes about two or three hours per deployment on an NVIDIA TITAN V. ", + "bbox": [ + 174, + 160, + 825, + 311 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "To leverage neural networks as Dyna-style (Sutton, 1991) dynamics models, we modify reward and termination function so that they are not dependent on the internal physics engine for calculation, following model-based benchmark codebase (Wang et al., 2019); see Table 3. Note that the score of baselines (e.g., BCQ, BRAC) is slightly different from Wu et al. (2019) due to this modification of the reward function. We re-run each algorithm in our environments and got appropriate convergence. ", + "bbox": [ + 174, + 319, + 825, + 388 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "The maximum length of one episode is 1,000 steps without any termination in Ant and HalfCheetah; however, termination function is enabled in Hopper and Walker2d. The batch size of transitions for policy update is 50,000 in BREMEN and ME-TRPO, following Kurutach et al. (2018). The batch size of BC and BRAC is 256, and BCQ is 100, also following Wu et al. (2019). ", + "bbox": [ + 174, + 395, + 825, + 452 + ], + "page_idx": 17 + }, + { + "type": "image", + "img_path": "images/22074d9a93978e2e7c0e5f01935d55d8e4c33f912df142778c7e453a465f0dca.jpg", + "image_caption": [ + "Figure 7: Four standard MuJoCo benchmark environments used in our experiments. " + ], + "image_footnote": [], + "bbox": [ + 228, + 477, + 771, + 597 + ], + "page_idx": 17 + }, + { + "type": "table", + "img_path": "images/c3dfc3126e61a5575c4040b8e48f97532d206a09c9889e721728d3fd7fd2dcf6.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3: Reward function and termination in rollouts in the experiments. We remove all contact information from observation of Ant, basically following Wang et al. (2019). " + ], + "table_body": "
EnvironmentRewardfunctionTerminationinrollouts
Antxt -0.1||atl²2-3.0 × (zt -0.57)² +1False
HalfCheetahxt -0.1||atll2False
Hopperxt - 0.001||atl2²+1True
Walker2dxt-0.001||atl2+1True
", + "bbox": [ + 209, + 636, + 789, + 714 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "F.2 HYPER PARAMETERS ", + "text_level": 1, + "bbox": [ + 174, + 103, + 362, + 118 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "In this section, we describe the hyper-parameters in both deployment-efficient RL (Section F.2.1) and offline RL (Section F.2.2) settings. We run all of our experiments with five random seed, and the results are averaged. ", + "bbox": [ + 174, + 128, + 825, + 172 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "F.2.1 DEPLOYMENT-EFFICIENT RL ", + "text_level": 1, + "bbox": [ + 174, + 186, + 429, + 202 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Table 4 shows the hyper-parameters of BREMEN. The rollout length is searched from {250, 500, $1 0 0 0 \\}$ , and max step size $\\delta$ is searched from {0.001, 0.01, 0.05, 0.1, 1.0}. As for the discount factor $\\gamma$ and GAE $\\lambda$ , we follow Wang et al. (2019). ", + "bbox": [ + 176, + 210, + 823, + 253 + ], + "page_idx": 18 + }, + { + "type": "table", + "img_path": "images/5bde77e082d02bae1f8f57063a505c8389660c84c3e31f5bf115066a97eec5d1.jpg", + "table_caption": [], + "table_footnote": [ + "Table 4: Hyper-parameters of BREMEN in deployment-efficient settings. " + ], + "table_body": "
ParameterAntHalfCheetahHopperWalker2d
Iteration per batch2,0002,0006.0002,000
Deployment551010
Total iteration10.00010.00060.00020.000
Rollouts length2502501,0001,000
Max step size δ0.050.10.050.05
Discount factor y0.990.990.990.99
GAE入0.970.950.950.95
Stationary noise o0.10.10.10.1
", + "bbox": [ + 276, + 267, + 720, + 386 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Number of Iterations for Policy Optimization To achieve high deployment efficiency, the number of iterations for policy optimization between deployments is one of the important hyper-parameters for fast convergence. In the existing methods (BCQ, BRAC, SAC), we search over three values: {10,000, 50,000, 100,000}, and choose 10,000 in BCQ and BRAC, and 100,000 in SAC (Figure 8). For BREMEN, we also search over three values: {2,000, 4,000, 6,000}. Figure 9 shows the results of iteration search, and we choose 2,000 in Ant, HalfCheetah, and Walker2d, and 6,000 in Hopper. ", + "bbox": [ + 173, + 426, + 826, + 511 + ], + "page_idx": 18 + }, + { + "type": "image", + "img_path": "images/e336bd4ed3f1cc2665e6fc99ab776b4c797ca110856fae70c3856d98bed9c733.jpg", + "image_caption": [ + "Figure 8: Search on the number of iterations for SAC policy optimization between deployments. The number of transitions per one data-collection is $2 0 0 \\mathrm { K }$ . " + ], + "image_footnote": [], + "bbox": [ + 189, + 529, + 812, + 640 + ], + "page_idx": 18 + }, + { + "type": "image", + "img_path": "images/e3aa31a1dfb8de492f2a7d1dd0ba0b09d7546b19b72131e2fcba0161b0bbc2a1.jpg", + "image_caption": [ + "Figure 9: Search on the number of iterations for BREMEN policy optimization between deployments. The number of transitions per one data-collection is 200K. " + ], + "image_footnote": [], + "bbox": [ + 187, + 696, + 810, + 808 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Stationary Noise in BREMEN To achieve effective exploration, the stochastic Gaussian policy is a good choice. We found that adding stationary Gaussian noise to the policy in the imaginary trajectories and data collection led to the notable improvement. Stationary Gaussian policy is written as, ", + "bbox": [ + 173, + 103, + 825, + 159 + ], + "page_idx": 19 + }, + { + "type": "equation", + "img_path": "images/1486e0d667bf2f8e17e0cefd8e07b39e41c2baf506d7618fd466feb8080a194d.jpg", + "text": "$$\na _ { t } = \\operatorname { t a n h } ( \\mu _ { \\theta } ( s _ { t } ) ) + \\epsilon , \\qquad \\epsilon \\sim \\mathcal { N } ( 0 , \\sigma ^ { 2 } ) .\n$$", + "text_format": "latex", + "bbox": [ + 354, + 156, + 643, + 175 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "Another choice is a learned Gaussian policy, which parameterizes not only $\\mu _ { \\theta }$ but also $\\sigma _ { \\theta }$ . Learned gaussian policy is also written as, ", + "bbox": [ + 171, + 178, + 823, + 207 + ], + "page_idx": 19 + }, + { + "type": "equation", + "img_path": "images/398fcde4eaed74b5a84d11c3a19eb0c34bd1dd1bba4a64a1aaccbee32ce8a45e.jpg", + "text": "$$\na _ { t } = \\operatorname { t a n h } ( \\mu _ { \\theta } ( s _ { t } ) ) + \\sigma _ { \\theta } ( s _ { t } ) \\odot \\epsilon , \\qquad \\epsilon \\sim \\mathcal { N } ( 0 , \\sigma ^ { 2 } ) .\n$$", + "text_format": "latex", + "bbox": [ + 323, + 212, + 674, + 231 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "We utilize the zero-mean Gaussian ${ \\mathcal { N } } ( 0 , \\sigma ^ { 2 } )$ , and tune up $\\sigma$ in Figure 10 with HalfCheetah, comparing stationary and learned strategies. From this experiment, we found that the stationary noise, the scale of 0.1, consistently performs well, and therefore we used it for all our experiments. ", + "bbox": [ + 174, + 236, + 826, + 279 + ], + "page_idx": 19 + }, + { + "type": "image", + "img_path": "images/e7fbb1985511ad7e639f10932800c9a46a2e1ab41d3aa44609db46b5b84b8f7d.jpg", + "image_caption": [ + "Figure 10: Search on the Gaussian noise parameter $\\sigma$ in HalfCheetah. The number of transitions per one data-collection is 200K. " + ], + "image_footnote": [], + "bbox": [ + 269, + 295, + 725, + 479 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "Other Hyper-parameters in the Existing Methods As for online ME-TRPO, we collect 3,000 steps through online interaction with the environment per 25 iterations and split these transitions into a 2-to-1 ratio of training and validation dataset for learning dynamics models. In batch size 100,000 settings, we collect 2,000 steps and split with 1-to-1 ratio. Totally, we iterate 12,500 times policy optimization, which is equivalent to 500 deployments of the policy. Note that we carefully tune up the hyper-parameters of online ME-TRPO, and the performance is improved from Wang et al. (2019). ", + "bbox": [ + 173, + 539, + 825, + 623 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "Table 5 and Table 6 shows the tunable hyper-parameters of BCQ and BRAC, respectively. We refer Wu et al. (2019) to choose these values. In this work, BRAC applies a primal form of KL value penalty, and BRAC (max Q) means sampling multiple actions and taking the maximum according to the learned Q function. ", + "bbox": [ + 174, + 630, + 825, + 686 + ], + "page_idx": 19 + }, + { + "type": "table", + "img_path": "images/2dc726091fb37dcc6a4987593fc89d0964cd16c8650d4f3f0031be344dce1213.jpg", + "table_caption": [ + "Table 5: Hyper-parameters of BCQ. " + ], + "table_footnote": [], + "table_body": "
ParameterAntHalfCheetahHopperWalker2d
Policy learning rate3e-053e-043e-063e-05
Perturbation range Φ0.150.50.150.15
", + "bbox": [ + 272, + 699, + 722, + 742 + ], + "page_idx": 19 + }, + { + "type": "table", + "img_path": "images/cef09bad5b8d3e3b5d0b86ce182a0c4eaca4c96fbcfb6f4abd7c8531617b6820.jpg", + "table_caption": [ + "Table 6: Hyper-parameters of BRAC. " + ], + "table_footnote": [], + "table_body": "
ParameterAntHalfCheetahHopperWalker2d
Policy learning rate1e-41e-33e-51e-5
Divergence penalty α0.30.10.30.3
", + "bbox": [ + 276, + 782, + 722, + 824 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "F.2.2 OFFLINE RL ", + "text_level": 1, + "bbox": [ + 174, + 103, + 313, + 117 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "In the offline experiments, we apply the same hyper-parameters as in the deployment-efficient settings described above, except for the iteration per batch. Algorithm 2 is pseudocode for BREMEN in offline RL settings where policies are updated only with one fixed batch dataset. The number of iteration $T$ is set to 6,250 in BREMEN, and 500,000 in BC, BCQ, and BRAC. ", + "bbox": [ + 174, + 127, + 825, + 184 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "The datasets for $5 0 \\mathrm { k }$ or $1 0 0 \\mathrm { k }$ experiments are sliced from the beginning of the 1M batched datasets without shuffling, but we observed that the distribution of rewards in 50k or $1 0 0 \\mathrm { k }$ is not different from 1M. ", + "bbox": [ + 174, + 190, + 823, + 233 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "Algorithm 2 BREMEN for Offline RL ", + "text_level": 1, + "bbox": [ + 174, + 246, + 413, + 261 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "Input: Offline dataset $\\mathcal { D } = \\{ s _ { t } , a _ { t } , r _ { t } , s _ { t + 1 } \\}$ , Initial parameters $\\phi = \\{ \\phi _ { 1 } , \\cdot \\cdot \\cdot , \\phi _ { K } \\}$ , $\\beta$ , Number of policy optimization $T$ . \n1: Train $K$ dynamics models $\\hat { f } _ { \\phi }$ using $\\mathcal { D }$ via Equation 1. \n2: Train estimated behavior policy $\\hat { \\pi } _ { \\beta }$ using $\\mathcal { D }$ by behavior cloning via Equation 3. \n3: Initialize target policy $\\pi _ { \\theta _ { 0 } } = \\mathrm { N o r m a l } ( \\hat { \\pi } _ { \\beta } , 1 )$ . \n4: for policy optimization $k = 1 , \\cdots , T$ do \n5: Generate imaginary rollout. \n6: Optimize target policy $\\pi \\theta$ satisfying Equation 4 with the rollout. ", + "bbox": [ + 176, + 265, + 825, + 372 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "G ADDITIONAL EXPERIMENTAL RESULTS ", + "text_level": 1, + "bbox": [ + 174, + 102, + 539, + 118 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "G.1 PERFORMANCE ON THE DATASET WITH DIFFERENT NOISE ", + "bbox": [ + 176, + 133, + 622, + 148 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "Following Wu et al. (2019) and Kidambi et al. (2020), we additionally compare BREMEN in offline settings to the other baselines (BC, BCQ, BRAC) with five datasets of different exploration noise. Each dataset has also one million transitions. ", + "bbox": [ + 176, + 159, + 826, + 202 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "• eps1: $40 \\%$ of the dataset is collected by data-collection policy (partially trained SAC policy) $\\pi _ { b }$ , $40 \\%$ of the dataset is collected by epsilon greedy policy with $\\epsilon = 0 . 1$ to take a random action, and $20 \\%$ of dataset is collected by an uniformly random policy. \n• eps3: Same as eps1, $40 \\%$ of the dataset is collected by $\\pi _ { b }$ , $40 \\%$ is collected by epsilon greedy policy with $\\epsilon = 0 . 3$ , and $20 \\%$ is collected by an uniformly random policy. gaussian1: $40 \\%$ of the dataset is collected by data-collection policy $\\pi _ { b }$ , $40 \\%$ is collected by the policy with adding zero-mean Gaussian noise $\\mathcal { N } ( 0 , 0 . \\bar { 1 } ^ { 2 } )$ to each action sampled from $\\pi _ { b }$ , and $20 \\%$ is collected by an uniformly random policy. \n• gaussian3: $40 \\%$ of the dataset is collected by data-collection policy $\\pi _ { b }$ , $40 \\%$ is collected by the policy with zero-mean Gaussian noise $\\bar { \\mathcal { N } ( 0 , 0 . 3 ^ { 2 } ) }$ , and $20 \\%$ is collected by an uniformly random policy. \n• random: All of the dataset is collected by an uniformly random policy. ", + "bbox": [ + 215, + 213, + 825, + 401 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "Table 7 shows that BREMEN can also achieve performance competitive with state-of-the-art modelfree offline RL algorithm even with noisy datasets. The training curves of each experiment are shown in Appendix G.4. ", + "bbox": [ + 174, + 412, + 826, + 454 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "G.2 COMPARISON AMONG DIFFERENT NUMBER OF ENSEMBLES", + "text_level": 1, + "bbox": [ + 176, + 470, + 632, + 486 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "To deal with the distribution shift during policy optimization, also known as model bias, we introduce the dynamics model ensembles. We validate the performance of BREMEN with a different number of dynamics models $K$ . Figure 11 and Figure 12 show the performance of BREMEN with the different number of ensembles in deployment-efficient and offline settings. Ensembles with more dynamics models resulted in better performance due to the mitigation of distributional shift except for $K = 1 0$ , and then we choose $K = 5$ . ", + "bbox": [ + 173, + 497, + 826, + 580 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/6a0b7f3bfe2cb62d53bb5b1256c8a3eb377aa3e705d405e2f33cc4f47577999d.jpg", + "image_caption": [ + "Figure 11: Comparison of the number of dynamics models in deployment-efficient settings. " + ], + "image_footnote": [], + "bbox": [ + 191, + 597, + 808, + 708 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/4755817929bd8db982519e32692cfd6b1d33c3aabe852221237d9bf32a39226b.jpg", + "image_caption": [ + "Figure 12: Comparison of the number of dynamics models in offline settings. " + ], + "image_footnote": [], + "bbox": [ + 191, + 752, + 808, + 863 + ], + "page_idx": 21 + }, + { + "type": "table", + "img_path": "images/88aced6a34cb4f97ea91ae388e1e86d3382eadf9999fc3997ee8d8ad4d836b10.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Noise: eps1,1,000,000 (1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset10772936791815
BC1381±713788±740266±4861185±155
BCQ1937±1166046±276800±659479±537
BRAC2693±1557003±1181243±1623204±103
BRAC (max Q)2907±987070±811488±3863330±147
BREMEN (Ours)3519±1297585±4252818±761710±429
ME-TRPO (offline)1514±5031009±7311301±654128±153
", + "bbox": [ + 251, + 180, + 746, + 296 + ], + "page_idx": 22 + }, + { + "type": "table", + "img_path": "images/ea8f638bbf7ff6349d977a1d93087eacd6ddcf16af53ed9bbe789657b09ce501.jpg", + "table_caption": [ + "Noise: eps3, 1,000,000 (1M) transitions " + ], + "table_footnote": [], + "table_body": "
MethodAntHalfCheetahHopperWalker2d
Dataset BC BCQ BRAC936 1364±121 1938±21 2718±90 2913±872408 2877±797 5739±188 6434±147662 519±532 1170±446 1224±71648 1066±176 1018±1231 2921±101
", + "bbox": [ + 251, + 308, + 745, + 411 + ], + "page_idx": 22 + }, + { + "type": "table", + "img_path": "images/a5c60f6d4dc2d15f32b77b3fe51506190ea36462050828690ddcd22320f35c19.jpg", + "table_caption": [ + "Noise: gaussian1, 1,000,000 (1M) transitions " + ], + "table_footnote": [], + "table_body": "
MethodAntHalfCheetahHopperWalker2d
Dataset107231508821070
BC1279±804142±18931±161137±477
BCQ1958±765854±498475±416608±416
BRAC2905±817026±1681456±1613030±103
BRAC (max Q)2910±1577026±1681575±893242±97
BREMEN (Ours)2912±1657928±3131999±6171402±290
ME-TRPO (offline)1275±6561275±656909±631171±119
", + "bbox": [ + 251, + 424, + 746, + 526 + ], + "page_idx": 22 + }, + { + "type": "table", + "img_path": "images/3efb47f42995fa78d09c7030250bb993ff41c7fa338cfb246aaf3d62b47b7b86.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Noise:gaussian3,1,0oo,0oo (1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset10582872781981
BC1300±344190±69611±4671217±361
BCQ1982±975781±5431137±582258±286
BRAC3084±1803933±27401432±4993253±118
BRAC (max Q)2916±993997±27611417±2673372±153
BREMEN (Ours)3432±1858124±1451867±3542299±474
ME-TRPO (offline)1237±3102141±872973±243219±145
", + "bbox": [ + 251, + 530, + 746, + 643 + ], + "page_idx": 22 + }, + { + "type": "table", + "img_path": "images/a5420d75a03349ea446e7f88e19e3708dd033674ec3b139281345a003d9b9ae8.jpg", + "table_caption": [ + "Noise: random, 1,000,000 (1M) transitions " + ], + "table_footnote": [ + "Table 7: Comparison of BREMEN to the existing offline methods in offline settings, namely, BC, BCQ (Fujimoto et al., 2019), and BRAC (Wu et al., 2019). Each cell shows the average cumulative reward and their standard deviation with 5 seeds. The maximum steps per episode is 1,000. Five different types of exploration noise are introduced during the data collection, eps1, eps3, gaussian1, gaussian3, and random. BRAC applies a primal form of KL value penalty, and BRAC (max Q) means sampling multiple actions and taking the maximum according to the learned Q function. " + ], + "table_body": "
MethodAntHalfCheetahHopperWalker2d
Dataset470-285342
BC989±10-2±1106±62108±110
BCQ1222±1142887±242206±7228±12
BRAC1057±923449±259227±3029±54
BRAC (max Q)683±573418±171224±3726±50
BREMEN (Ours)905±113627±193270±68254±6
ME-TRPO (offline)2221±6652701±120321±29262±13
", + "bbox": [ + 250, + 655, + 746, + 761 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "G.3 IMPLICIT KL CONTROL IN OFFLINE SETTINGS ", + "text_level": 1, + "bbox": [ + 173, + 102, + 540, + 118 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Similar to Section 5.3, we present offline RL experiments to better understand the effect of implicit KL regularization. In contrast to the implicit KL regularization with Equation 4, the optimization of BREMEN with explicit KL value penalty becomes ", + "bbox": [ + 174, + 128, + 825, + 172 + ], + "page_idx": 23 + }, + { + "type": "equation", + "img_path": "images/ce620e6424c73535e915a205c5e5502c596ac9ad74d58381048c4a153f0eb809.jpg", + "text": "$$\n\\begin{array} { r l } & { \\theta _ { k + 1 } = \\underset { \\theta } { \\arg \\operatorname* { m a x } } \\ \\underset { s , a \\sim \\pi _ { \\theta _ { k } } , \\hat { f } _ { \\phi _ { i } } } { \\mathrm { E } } [ \\frac { \\pi _ { \\theta } ( a | s ) } { \\pi _ { \\theta _ { k } } ( a | s ) } ( A ^ { \\pi _ { \\theta _ { k } } } ( s , a ) - \\alpha D _ { \\mathrm { K L } } ( \\pi _ { \\theta } ( \\cdot | s ) | ) \\hat { \\pi } _ { \\beta } ( \\cdot | s ) ) ) ] } \\\\ & { \\quad \\mathrm { s . t . } \\quad \\underset { s \\sim \\pi _ { \\theta _ { k } } } { \\mathrm { E } } [ D _ { \\mathrm { K L } } ( \\pi _ { \\theta } ( \\cdot | s ) | | \\pi _ { \\theta _ { k } } ( \\cdot | s ) ) ] \\leq \\delta , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 232, + 178, + 764, + 243 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "where $A ^ { \\pi _ { \\theta _ { k } } } ( s , a )$ is the advantage of $\\pi _ { \\theta _ { k } }$ computed using imaginary rollouts with the learned dynamics model and $\\delta$ is the maximum step size. Note that BREMEN with explicit KL penalty does not utilize behavior cloning initialization. ", + "bbox": [ + 178, + 250, + 820, + 292 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "We empirically conclude that the explicit constraint $- \\alpha D _ { \\mathrm { K L } } \\big ( \\pi _ { \\boldsymbol { \\theta } } \\big ( \\cdot | \\boldsymbol { s } \\big ) \\big | \\big | \\hat { \\pi } _ { \\boldsymbol { \\beta } } \\big ( \\cdot | \\boldsymbol { s } \\big ) \\big )$ is unnecessary and just TRPO update with behavior-initialization as implicit regularization is sufficient in BREMEN algorithm. Figure 13 shows the KL divergence between learned policies and the last deployed policies (top row) and model errors measured by a mean squared error of predicted next state from the true state (second row). We find that behavior initialized policy with conservative KL trust-region updates well stuck to the last deployed policy during improvement without explicit KL penalty. The policy initialized with behavior cloning also tended to suppress the increase of model error, which implies that behavior initialization alleviates the effect of the distribution shift. In Walker2d, the model error of BREMEN is relatively large, which may relate to the poor performance with noisy datasets in Section G.1. ", + "bbox": [ + 173, + 297, + 825, + 438 + ], + "page_idx": 23 + }, + { + "type": "image", + "img_path": "images/380b79685657ca35961a182d8249d87b52383e893929db691d571c0225df1788.jpg", + "image_caption": [ + "Figure 13: Average cumulative rewards (top row) and corresponding KL divergence of learned policies from the last deployed policy (second row) and model errors (bottom row) in offline settings with 1M dataset (no noise). Behavior initialized policy (purple line) tends to suppress the policy and model error during training better than no-initialization (red line) or explicit KL penalty (green line). " + ], + "image_footnote": [], + "bbox": [ + 187, + 452, + 810, + 732 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "G.4 TRAINING CURVES FOR OFFLINE RL WITH DIFFERENT NOISES ", + "text_level": 1, + "bbox": [ + 174, + 103, + 656, + 118 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "In this section, we present training curves of our all experiments in offline settings. Figure 14 shows the results in Section 5.1. Figure 15, 16, 17, 18, and 19 also show the results in Section G.1. ", + "bbox": [ + 173, + 128, + 825, + 159 + ], + "page_idx": 24 + }, + { + "type": "image", + "img_path": "images/c5d8d3e93857b4772c71f9250ddb7e71a41d48a084aa8ff5d13896dcd60f0009.jpg", + "image_caption": [ + "Figure 14: Performance in Offline RL experiments (Table 1). (top row) dataset size is 1M, (second row) 100K, and (bottom row) 50K, respectively. Note that $\\mathbf { X }$ -axis is the number of iterations with policy optimization in a log-scale. " + ], + "image_footnote": [], + "bbox": [ + 189, + 172, + 810, + 468 + ], + "page_idx": 24 + }, + { + "type": "image", + "img_path": "images/d9bc704351f20f3bf3fe30910804c40f1535b0cbc6b7b20c34aaf8f4523b2285.jpg", + "image_caption": [ + "Figure 15: Performance in Offline RL experiments with $\\epsilon$ -greedy dataset noise $\\epsilon = 0 . 1$ . Dataset size is 1M. " + ], + "image_footnote": [], + "bbox": [ + 191, + 536, + 808, + 650 + ], + "page_idx": 24 + }, + { + "type": "image", + "img_path": "images/f7f775ecb6dd3a924b4eb9058d7436ed3071014842ad90e854f68d8851a101b6.jpg", + "image_caption": [ + "Figure 16: Performance in Offline RL experiments with $\\epsilon$ -greedy dataset noise $\\epsilon = 0 . 3$ . Dataset size is 1M. " + ], + "image_footnote": [], + "bbox": [ + 191, + 694, + 808, + 806 + ], + "page_idx": 24 + }, + { + "type": "image", + "img_path": "images/130499bcf5e465aeeb59cee68e4a26cc2b0724c07bdd0d5ddaf94eaa44e62ee8.jpg", + "image_caption": [ + "Figure 17: Performance in Offline RL experiments with gaussian dataset noise $\\mathcal { N } ( 0 , 0 . 1 ^ { 2 } )$ . Dataset size is 1M. " + ], + "image_footnote": [], + "bbox": [ + 189, + 171, + 808, + 282 + ], + "page_idx": 25 + }, + { + "type": "image", + "img_path": "images/b5e14c327508062c360ef17f8d7d6f8358413758c78deda33a2faba939bb6d82.jpg", + "image_caption": [ + "Figure 18: Performance in Offline RL experiments with gaussian dataset noise $\\mathcal { N } ( 0 , 0 . 3 ^ { 2 } )$ . Dataset size is 1M. " + ], + "image_footnote": [], + "bbox": [ + 191, + 448, + 808, + 559 + ], + "page_idx": 25 + }, + { + "type": "image", + "img_path": "images/e8bd3de5b194349afabaa366a65cff854f71e8cdf7495f71533961a224245881.jpg", + "image_caption": [ + "Figure 19: Performance in Offline RL experiments with completely random behaviors. Dataset size is 1M. " + ], + "image_footnote": [], + "bbox": [ + 191, + 723, + 808, + 835 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "G.5 DEPLOYMENT-EFFICIENT RL EXPERIMENT WITH DIFFERENT REWARD FUNCTION ", + "text_level": 1, + "bbox": [ + 169, + 103, + 789, + 118 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "In addition to the main results in Section 5.2 (Figure 2), we also evaluate BREMEN in deploymentefficient setting with different reward function. We modified HalfCheetah environment into the one similar to cheetah-run task in Deep Mind Control Suite.5 The reward function is defined as ", + "bbox": [ + 173, + 128, + 826, + 171 + ], + "page_idx": 26 + }, + { + "type": "equation", + "img_path": "images/7fcc04ad00beb4079f7af7b1ac686011f5d205f51c984d1fda920384d2e971df.jpg", + "text": "$$\nr _ { t } = \\left\\{ \\begin{array} { l l } { 0 . 1 \\dot { x } _ { t } } & { ( 0 \\leq \\dot { x } _ { t } \\leq 1 0 ) } \\\\ { 1 } & { ( \\dot { x } _ { t } > 1 0 ) , } \\end{array} \\right.\n$$", + "text_format": "latex", + "bbox": [ + 398, + 179, + 598, + 215 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "and the termination is turned off. Figure 20 shows the performance of BREMEN and existing methods. BREMEN also shows better deployment efficiency than other existing offline methods and online ME-TRPO, except for SAC, which is the same trend as that of main results. ", + "bbox": [ + 174, + 222, + 825, + 265 + ], + "page_idx": 26 + }, + { + "type": "image", + "img_path": "images/dd467a13475aaa5cb2f106904be422eee8725c7d1362d2167e7a9ddb7c8b3d1c.jpg", + "image_caption": [ + "Figure 20: Performance in Deployment-Efficient RL experiments with different reward function of HalfCheetah. 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Virtually all of these demonstrations have relied on highly-frequent", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 561, + 505, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 505, + 577 + ], + "score": 1.0, + "content": "online access to the environment, with the RL algorithms often interleaving each update to the policy", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 574, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 106, + 574, + 505, + 586 + ], + "score": 1.0, + "content": "with additional experience collection of that policy acting in the environment. However, in many", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 586, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 586, + 505, + 597 + ], + "score": 1.0, + "content": "real-world applications of RL, such as health (Murphy et al., 2001), education (Mandel et al., 2014),", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 596, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 506, + 609 + ], + "score": 1.0, + "content": "dialog agents (Jaques et al., 2019), and robotics (Gu et al., 2017a; Kalashnikov et al., 2018), the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 608, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 106, + 608, + 505, + 619 + ], + "score": 1.0, + "content": "deployment of a new data-collection policy may be associated with a number of costs and risks. If", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 618, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 618, + 506, + 631 + ], + "score": 1.0, + "content": "we can learn tasks with a small number of data collection policies, we can substantially reduce them.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 529, + 506, + 631 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 635, + 504, + 701 + ], + "lines": [ + { + "bbox": [ + 105, + 634, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 506, + 648 + ], + "score": 1.0, + "content": "Based on this idea, we propose a novel measure of RL algorithm performance, namely deployment", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 646, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 106, + 646, + 506, + 658 + ], + "score": 1.0, + "content": "efficiency, which counts the number of changes in the data-collection policy during learning, as illus-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 655, + 506, + 671 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 671 + ], + "score": 1.0, + "content": "trated in Figure 1. This concept may be seen in contrast to sample efficiency or data efficiency (Precup", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 668, + 506, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 506, + 680 + ], + "score": 1.0, + "content": "et al., 2001; Degris et al., 2012; Gu et al., 2017b; Haarnoja et al., 2018; Lillicrap et al., 2016; Nachum", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 678, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 506, + 691 + ], + "score": 1.0, + "content": "et al., 2018), which measures the amount of environment interactions incurred during training, without", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 690, + 505, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 690, + 505, + 702 + ], + "score": 1.0, + "content": "regard to how many distinct policies were deployed to perform those interactions. Even when the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 336, + 504, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 504, + 348 + ], + "score": 1.0, + "content": "data efficiency is high, the deployment efficiency could be low, since many on-policy and off-policy", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 346, + 506, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 506, + 360 + ], + "score": 1.0, + "content": "algorithms alternate data collection with each policy update (Schulman et al., 2015; Lillicrap et al.,", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 358, + 504, + 370 + ], + "spans": [ + { + "bbox": [ + 106, + 358, + 504, + 370 + ], + "score": 1.0, + "content": "2016; Gu et al., 2016; Haarnoja et al., 2018). Such dependence on high-frequency policy deployments", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 369, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 106, + 369, + 505, + 380 + ], + "score": 1.0, + "content": "is best illustrated in the recent works in offline RL (Fujimoto et al., 2019; Jaques et al., 2019; Kumar", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 380, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 380, + 505, + 392 + ], + "score": 1.0, + "content": "et al., 2019; Levine et al., 2020; Wu et al., 2019), where baseline off-policy algorithms exhibited poor", + "type": "text", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "score": 1.0, + "content": "performance when trained on a static dataset. These offline RL works, however, limit their study to", + "type": "text", + "cross_page": true + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 402, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 106, + 402, + 506, + 414 + ], + "score": 1.0, + "content": "a single deployment, which is enough for achieving high performance with data collected from a", + "type": "text", + "cross_page": true + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 412, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 505, + 425 + ], + "score": 1.0, + "content": "sub-optimal behavior policy, but often not from a random policy. In contrast to those prior works, we", + "type": "text", + "cross_page": true + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 424, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 506, + 436 + ], + "score": 1.0, + "content": "aim to learn successful policies from scratch in a manner that is both sample and deployment-efficient.", + "type": "text", + "cross_page": true + } + ], + "index": 19 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 634, + 506, + 702 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 130, + 79, + 486, + 205 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 130, + 79, + 486, + 205 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 130, + 79, + 486, + 205 + ], + "spans": [ + { + "bbox": [ + 130, + 79, + 486, + 205 + ], + "score": 0.975, + "type": "image", + "image_path": "d4b7db2b7c0236b75d1498e37817a81892cf444ccaaf33effb12564d6ca2dc21.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 130, + 79, + 486, + 121.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 130, + 121.0, + 486, + 163.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 130, + 163.0, + 486, + 205.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 209, + 506, + 289 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 208, + 505, + 219 + ], + "spans": [ + { + "bbox": [ + 106, + 208, + 465, + 219 + ], + "score": 1.0, + "content": "Figure 1: Deployment efficiency is defined as the number of changes in the data-collection policy", + "type": "text" + }, + { + "bbox": [ + 465, + 209, + 476, + 219 + ], + "score": 0.52, + "content": "( I )", + "type": "inline_equation" + }, + { + "bbox": [ + 477, + 208, + 505, + 219 + ], + "score": 1.0, + "content": ", which", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 217, + 506, + 231 + ], + "spans": [ + { + "bbox": [ + 104, + 217, + 506, + 231 + ], + "score": 1.0, + "content": "is vital for managing costs and risks of new policy deployment. Online RL algorithms typically require", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 227, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 104, + 227, + 506, + 241 + ], + "score": 1.0, + "content": "many iterations of policy deployment and data collection, which leads to extremely low deployment efficiency.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 238, + 505, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 238, + 505, + 250 + ], + "score": 1.0, + "content": "In contrast, most pure offline algorithms consider updating a policy from a fixed dataset without additional", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 248, + 506, + 260 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 506, + 260 + ], + "score": 1.0, + "content": "deployment and often fail to learn from a randomly initialized data-collection policy. Interestingly, most", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 258, + 506, + 271 + ], + "spans": [ + { + "bbox": [ + 104, + 258, + 506, + 271 + ], + "score": 1.0, + "content": "state-of-the-art off-policy algorithms are still evaluated in heavily online settings. For example, SAC (Haarnoja", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 267, + 506, + 281 + ], + "spans": [ + { + "bbox": [ + 104, + 267, + 506, + 281 + ], + "score": 1.0, + "content": "et al., 2018) collects one sample per policy update, amounting to 100,000 to 1 million deployments for learning", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 278, + 217, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 278, + 217, + 290 + ], + "score": 1.0, + "content": "standard benchmark domains.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6.5 + } + ], + "index": 3.75 + }, + { + "type": "text", + "bbox": [ + 106, + 335, + 505, + 435 + ], + "lines": [ + { + "bbox": [ + 106, + 336, + 504, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 504, + 348 + ], + "score": 1.0, + "content": "data efficiency is high, the deployment efficiency could be low, since many on-policy and off-policy", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 346, + 506, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 506, + 360 + ], + "score": 1.0, + "content": "algorithms alternate data collection with each policy update (Schulman et al., 2015; Lillicrap et al.,", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 358, + 504, + 370 + ], + "spans": [ + { + "bbox": [ + 106, + 358, + 504, + 370 + ], + "score": 1.0, + "content": "2016; Gu et al., 2016; Haarnoja et al., 2018). Such dependence on high-frequency policy deployments", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 369, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 106, + 369, + 505, + 380 + ], + "score": 1.0, + "content": "is best illustrated in the recent works in offline RL (Fujimoto et al., 2019; Jaques et al., 2019; Kumar", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 380, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 380, + 505, + 392 + ], + "score": 1.0, + "content": "et al., 2019; Levine et al., 2020; Wu et al., 2019), where baseline off-policy algorithms exhibited poor", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "score": 1.0, + "content": "performance when trained on a static dataset. These offline RL works, however, limit their study to", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 402, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 106, + 402, + 506, + 414 + ], + "score": 1.0, + "content": "a single deployment, which is enough for achieving high performance with data collected from a", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 412, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 505, + 425 + ], + "score": 1.0, + "content": "sub-optimal behavior policy, but often not from a random policy. In contrast to those prior works, we", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 424, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 506, + 436 + ], + "score": 1.0, + "content": "aim to learn successful policies from scratch in a manner that is both sample and deployment-efficient.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 441, + 505, + 605 + ], + "lines": [ + { + "bbox": [ + 105, + 440, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 505, + 452 + ], + "score": 1.0, + "content": "Many existing model-free offline RL algorithms (Levine et al., 2020) are tuned and evaluated on", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 451, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 505, + 464 + ], + "score": 1.0, + "content": "massive datasets (e.g., one million transitions). In order to develop an algorithm that is both sample", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "and deployment-efficient, each iteration of the algorithm between successive deployments has to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 473, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 505, + 486 + ], + "score": 1.0, + "content": "work effectively on much smaller dataset sizes. We believe model-based RL is better suited to", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 484, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 505, + 497 + ], + "score": 1.0, + "content": "this setting due to its higher demonstrated sample efficiency than model-free RL (Kurutach et al.,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 495, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 506, + 507 + ], + "score": 1.0, + "content": "2018; Nagabandi et al., 2018). Although the combination of model-based RL and offline or limited-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 506, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 506, + 519 + ], + "score": 1.0, + "content": "deployment settings seems straight-forward, we find this naïve approach leads to poor performance.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 517, + 506, + 530 + ], + "spans": [ + { + "bbox": [ + 106, + 517, + 506, + 530 + ], + "score": 1.0, + "content": "This problem can be attributed to extrapolation errors (Fujimoto et al., 2019) similar to those observed", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 528, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 505, + 540 + ], + "score": 1.0, + "content": "in model-free methods. Specifically, the learned policy may choose sequences of actions which", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 538, + 506, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 506, + 552 + ], + "score": 1.0, + "content": "lead it to regions of the state space where the dynamics model cannot predict properly, due to poor", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 550, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 505, + 563 + ], + "score": 1.0, + "content": "coverage of the dataset. This can lead the policy to exploit approximation errors of the dynamics", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 561, + 504, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 504, + 573 + ], + "score": 1.0, + "content": "model and be disastrous for learning. In model-free settings, similar data distribution shift problems", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 505, + 585 + ], + "score": 1.0, + "content": "are typically remedied by regularizing policy updates explicitly with a divergence from the observed", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 582, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 505, + 595 + ], + "score": 1.0, + "content": "data distribution (Jaques et al., 2019; Kumar et al., 2019; Wu et al., 2019), which, however, can overly", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 594, + 293, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 293, + 606 + ], + "score": 1.0, + "content": "limit policies’ expressivity (Sohn et al., 2020).", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 611, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 611, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 505, + 624 + ], + "score": 1.0, + "content": "In order to better approach these problems arising in limited deployment settings, we propose", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 621, + 505, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 634 + ], + "score": 1.0, + "content": "Behavior-Regularized Model-ENsemble (BREMEN), which learns an ensemble of dynamics models", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 632, + 505, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 647 + ], + "score": 1.0, + "content": "in conjunction with a policy using imaginary rollouts while implicitly regularizing the learned policy", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 644, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 657 + ], + "score": 1.0, + "content": "via appropriate parameter initialization and conservative trust-region learning updates. We evaluate", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "BREMEN on standard offline RL benchmarks of high-dimensional continuous control tasks, where", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "only a single static dataset is used. In this fixed-batch setting, our experiments show that BREMEN", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "can not only achieve performance competitive with state-of-the-art when using standard dataset sizes", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "score": 1.0, + "content": "but also learn with 10-20 times smaller datasets, which previous methods are unable to attain. Enabled", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "by such stable and sample-efficient offline learning, we show that BREMEN can learn successful", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "score": 1.0, + "content": "policies with only 5-10 deployments in the online setting, significantly outperforming existing", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 720, + 487, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 487, + 734 + ], + "score": 1.0, + "content": "off-policy and offline RL algorithms in deployment efficiency while keeping sample efficiency.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 40 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 292, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "score": 1.0, + "content": "2", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 130, + 79, + 486, + 205 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 130, + 79, + 486, + 205 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 130, + 79, + 486, + 205 + ], + "spans": [ + { + "bbox": [ + 130, + 79, + 486, + 205 + ], + "score": 0.975, + "type": "image", + "image_path": "d4b7db2b7c0236b75d1498e37817a81892cf444ccaaf33effb12564d6ca2dc21.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 130, + 79, + 486, + 121.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 130, + 121.0, + 486, + 163.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 130, + 163.0, + 486, + 205.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 209, + 506, + 289 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 208, + 505, + 219 + ], + "spans": [ + { + "bbox": [ + 106, + 208, + 465, + 219 + ], + "score": 1.0, + "content": "Figure 1: Deployment efficiency is defined as the number of changes in the data-collection policy", + "type": "text" + }, + { + "bbox": [ + 465, + 209, + 476, + 219 + ], + "score": 0.52, + "content": "( I )", + "type": "inline_equation" + }, + { + "bbox": [ + 477, + 208, + 505, + 219 + ], + "score": 1.0, + "content": ", which", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 217, + 506, + 231 + ], + "spans": [ + { + "bbox": [ + 104, + 217, + 506, + 231 + ], + "score": 1.0, + "content": "is vital for managing costs and risks of new policy deployment. Online RL algorithms typically require", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 227, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 104, + 227, + 506, + 241 + ], + "score": 1.0, + "content": "many iterations of policy deployment and data collection, which leads to extremely low deployment efficiency.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 238, + 505, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 238, + 505, + 250 + ], + "score": 1.0, + "content": "In contrast, most pure offline algorithms consider updating a policy from a fixed dataset without additional", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 248, + 506, + 260 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 506, + 260 + ], + "score": 1.0, + "content": "deployment and often fail to learn from a randomly initialized data-collection policy. Interestingly, most", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 258, + 506, + 271 + ], + "spans": [ + { + "bbox": [ + 104, + 258, + 506, + 271 + ], + "score": 1.0, + "content": "state-of-the-art off-policy algorithms are still evaluated in heavily online settings. For example, SAC (Haarnoja", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 267, + 506, + 281 + ], + "spans": [ + { + "bbox": [ + 104, + 267, + 506, + 281 + ], + "score": 1.0, + "content": "et al., 2018) collects one sample per policy update, amounting to 100,000 to 1 million deployments for learning", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 278, + 217, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 278, + 217, + 290 + ], + "score": 1.0, + "content": "standard benchmark domains.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6.5 + } + ], + "index": 3.75 + }, + { + "type": "text", + "bbox": [ + 106, + 335, + 505, + 435 + ], + "lines": [], + "index": 15, + "bbox_fs": [ + 105, + 336, + 506, + 436 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 441, + 505, + 605 + ], + "lines": [ + { + "bbox": [ + 105, + 440, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 505, + 452 + ], + "score": 1.0, + "content": "Many existing model-free offline RL algorithms (Levine et al., 2020) are tuned and evaluated on", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 451, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 505, + 464 + ], + "score": 1.0, + "content": "massive datasets (e.g., one million transitions). In order to develop an algorithm that is both sample", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "and deployment-efficient, each iteration of the algorithm between successive deployments has to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 473, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 505, + 486 + ], + "score": 1.0, + "content": "work effectively on much smaller dataset sizes. We believe model-based RL is better suited to", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 484, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 505, + 497 + ], + "score": 1.0, + "content": "this setting due to its higher demonstrated sample efficiency than model-free RL (Kurutach et al.,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 495, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 506, + 507 + ], + "score": 1.0, + "content": "2018; Nagabandi et al., 2018). Although the combination of model-based RL and offline or limited-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 506, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 506, + 519 + ], + "score": 1.0, + "content": "deployment settings seems straight-forward, we find this naïve approach leads to poor performance.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 517, + 506, + 530 + ], + "spans": [ + { + "bbox": [ + 106, + 517, + 506, + 530 + ], + "score": 1.0, + "content": "This problem can be attributed to extrapolation errors (Fujimoto et al., 2019) similar to those observed", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 528, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 505, + 540 + ], + "score": 1.0, + "content": "in model-free methods. Specifically, the learned policy may choose sequences of actions which", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 538, + 506, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 506, + 552 + ], + "score": 1.0, + "content": "lead it to regions of the state space where the dynamics model cannot predict properly, due to poor", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 550, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 505, + 563 + ], + "score": 1.0, + "content": "coverage of the dataset. This can lead the policy to exploit approximation errors of the dynamics", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 561, + 504, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 504, + 573 + ], + "score": 1.0, + "content": "model and be disastrous for learning. In model-free settings, similar data distribution shift problems", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 505, + 585 + ], + "score": 1.0, + "content": "are typically remedied by regularizing policy updates explicitly with a divergence from the observed", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 582, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 505, + 595 + ], + "score": 1.0, + "content": "data distribution (Jaques et al., 2019; Kumar et al., 2019; Wu et al., 2019), which, however, can overly", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 594, + 293, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 293, + 606 + ], + "score": 1.0, + "content": "limit policies’ expressivity (Sohn et al., 2020).", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 27, + "bbox_fs": [ + 105, + 440, + 506, + 606 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 611, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 611, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 505, + 624 + ], + "score": 1.0, + "content": "In order to better approach these problems arising in limited deployment settings, we propose", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 621, + 505, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 634 + ], + "score": 1.0, + "content": "Behavior-Regularized Model-ENsemble (BREMEN), which learns an ensemble of dynamics models", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 632, + 505, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 647 + ], + "score": 1.0, + "content": "in conjunction with a policy using imaginary rollouts while implicitly regularizing the learned policy", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 644, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 657 + ], + "score": 1.0, + "content": "via appropriate parameter initialization and conservative trust-region learning updates. We evaluate", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "BREMEN on standard offline RL benchmarks of high-dimensional continuous control tasks, where", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "only a single static dataset is used. 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Enabled", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "by such stable and sample-efficient offline learning, we show that BREMEN can learn successful", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "score": 1.0, + "content": "policies with only 5-10 deployments in the online setting, significantly outperforming existing", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 720, + 487, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 487, + 734 + ], + "score": 1.0, + "content": "off-policy and offline RL algorithms in deployment efficiency while keeping sample efficiency.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 611, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 207, + 93 + ], + "lines": [ + { + "bbox": [ + 105, + 80, + 209, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 209, + 96 + ], + "score": 1.0, + "content": "2 PRELIMINARIES", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 106, + 505, + 206 + ], + "lines": [ + { + "bbox": [ + 106, + 106, + 505, + 119 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 475, + 119 + ], + "score": 1.0, + "content": "We consider a Markov Decision Process (MDP) setting, characterized by the tuple", + "type": "text" + }, + { + "bbox": [ + 475, + 107, + 505, + 118 + ], + "score": 0.84, + "content": "\\begin{array} { r l } { \\mathcal { M } } & { { } = } \\end{array}", + "type": "inline_equation" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 116, + 506, + 131 + ], + "spans": [ + { + "bbox": [ + 106, + 118, + 161, + 129 + ], + "score": 0.91, + "content": "( S , \\mathcal { A } , p , r , \\gamma )", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 116, + 194, + 131 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 194, + 118, + 203, + 128 + ], + "score": 0.79, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 116, + 281, + 131 + ], + "score": 1.0, + "content": "is the state space,", + "type": "text" + }, + { + "bbox": [ + 281, + 118, + 290, + 128 + ], + "score": 0.72, + "content": "\\mathcal { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 116, + 374, + 131 + ], + "score": 1.0, + "content": "is the action space,", + "type": "text" + }, + { + "bbox": [ + 374, + 118, + 413, + 129 + ], + "score": 0.92, + "content": "p ( s ^ { \\prime } | s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 413, + 116, + 506, + 131 + ], + "score": 1.0, + "content": "is the transition prob-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 128, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 237, + 141 + ], + "score": 1.0, + "content": "ability distribution or dynamics,", + "type": "text" + }, + { + "bbox": [ + 237, + 129, + 256, + 141 + ], + "score": 0.92, + "content": "r ( s )", + "type": "inline_equation" + }, + { + "bbox": [ + 256, + 128, + 364, + 141 + ], + "score": 1.0, + "content": "is the reward function and", + "type": "text" + }, + { + "bbox": [ + 364, + 129, + 405, + 141 + ], + "score": 0.91, + "content": "\\gamma \\in ( 0 , 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 128, + 506, + 141 + ], + "score": 1.0, + "content": "is the discount factor. A", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 138, + 507, + 153 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 133, + 153 + ], + "score": 1.0, + "content": "policy", + "type": "text" + }, + { + "bbox": [ + 133, + 142, + 141, + 150 + ], + "score": 0.71, + "content": "\\pi", + "type": "inline_equation" + }, + { + "bbox": [ + 141, + 138, + 507, + 153 + ], + "score": 1.0, + "content": "is a function that determines the agent behavior, mapping from states to probability distribu-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 150, + 506, + 164 + ], + "spans": [ + { + "bbox": [ + 106, + 150, + 342, + 164 + ], + "score": 1.0, + "content": "tions over actions. 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The transition probability", + "type": "text" + }, + { + "bbox": [ + 325, + 162, + 363, + 173 + ], + "score": 0.93, + "content": "p ( s ^ { \\prime } | s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 161, + 506, + 174 + ], + "score": 1.0, + "content": "is usually unknown, and estimated", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 172, + 506, + 186 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 259, + 186 + ], + "score": 1.0, + "content": "with a parameterized dynamics model", + "type": "text" + }, + { + "bbox": [ + 260, + 173, + 271, + 185 + ], + "score": 0.87, + "content": "f _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 172, + 506, + 186 + ], + "score": 1.0, + "content": "(e.g. a neural network) in model-based RL. For simplicity,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 183, + 505, + 196 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 248, + 196 + ], + "score": 1.0, + "content": "we assume that the reward function", + "type": "text" + }, + { + "bbox": [ + 248, + 184, + 266, + 195 + ], + "score": 0.9, + "content": "r ( s )", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 183, + 505, + 196 + ], + "score": 1.0, + "content": "is known, and the reward can be computed for any arbitrary", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 194, + 483, + 207 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 483, + 207 + ], + "score": 1.0, + "content": "state, but we may extend to the unknown setting and predict it using a parameterized function.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 211, + 505, + 398 + ], + "lines": [ + { + "bbox": [ + 106, + 210, + 505, + 224 + ], + "spans": [ + { + "bbox": [ + 106, + 210, + 505, + 224 + ], + "score": 1.0, + "content": "On-policy vs Off-policy, Online vs Offline At a high-level, most RL algorithms alternate many", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 222, + 506, + 235 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 506, + 235 + ], + "score": 1.0, + "content": "times between collecting a batch of transitions (deployments) and optimizing the policy (learning).", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 232, + 506, + 246 + ], + "spans": [ + { + "bbox": [ + 105, + 232, + 506, + 246 + ], + "score": 1.0, + "content": "If the algorithms discard data after each policy update, they are on-policy (Schulman et al., 2015;", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 243, + 506, + 257 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 308, + 257 + ], + "score": 1.0, + "content": "2017), while if they accumulate data in a buffer", + "type": "text" + }, + { + "bbox": [ + 309, + 245, + 318, + 254 + ], + "score": 0.77, + "content": "\\mathcal { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 243, + 506, + 257 + ], + "score": 1.0, + "content": ", i.e. experience replay (Lin, 1992), they are", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 255, + 506, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 506, + 267 + ], + "score": 1.0, + "content": "off-policy (Mnih et al., 2015; Lillicrap et al., 2016; Gu et al., 2016; 2017b; Haarnoja et al., 2018;", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 266, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 505, + 277 + ], + "score": 1.0, + "content": "Fujimoto et al., 2019; Fakoor et al., 2019) because not all the data in buffer comes from the current", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 277, + 505, + 289 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 505, + 289 + ], + "score": 1.0, + "content": "policy. However, we consider all these algorithms to be online RL algorithms, since they involve", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 286, + 506, + 301 + ], + "spans": [ + { + "bbox": [ + 104, + 286, + 506, + 301 + ], + "score": 1.0, + "content": "many deployments during learning, ranging from hundreds to millions. On the other hand, in pure", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 299, + 507, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 507, + 311 + ], + "score": 1.0, + "content": "offline RL, one does not assume direct interaction and learns a policy from only a fixed dataset,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 309, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 505, + 323 + ], + "score": 1.0, + "content": "which effectively corresponds to a single deployment allowed for learning. Classically, interpolating", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 321, + 505, + 333 + ], + "spans": [ + { + "bbox": [ + 106, + 321, + 505, + 333 + ], + "score": 1.0, + "content": "these two extremes were semi-batch RL algorithms (Lange et al., 2012; Singh et al., 1995), which", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 331, + 504, + 344 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 428, + 344 + ], + "score": 1.0, + "content": "improve the policy through repetitions of collecting a large batch of transitions", + "type": "text" + }, + { + "bbox": [ + 428, + 332, + 504, + 344 + ], + "score": 0.94, + "content": "\\mathcal { D } = \\{ ( s , a , s ^ { \\prime } , r ) \\}", + "type": "inline_equation" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 343, + 505, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 505, + 356 + ], + "score": 1.0, + "content": "and performing many or full policy updates. While these semi-batch RL also realize good deployment", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 353, + 505, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 505, + 366 + ], + "score": 1.0, + "content": "efficiency, they have not been extensively studied with neural network function approximators or in", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 365, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 365, + 505, + 378 + ], + "score": 1.0, + "content": "off-policy settings with experience replay for scalable sample-efficient learning. In our work, we aim", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 375, + 505, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 505, + 389 + ], + "score": 1.0, + "content": "to have both high deployment efficiency and sample efficiency by developing an algorithm that can", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 386, + 422, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 422, + 399 + ], + "score": 1.0, + "content": "solve the tasks with minimal policy deployments as well as transition samples.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 18 + }, + { + "type": "title", + "bbox": [ + 109, + 415, + 262, + 428 + ], + "lines": [ + { + "bbox": [ + 105, + 414, + 264, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 414, + 264, + 430 + ], + "score": 1.0, + "content": "3 DEPLOYMENT EFFICIENCY", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 441, + 506, + 583 + ], + "lines": [ + { + "bbox": [ + 105, + 440, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 506, + 452 + ], + "score": 1.0, + "content": "Deploying a new policy for data collection can be associated with a number of costs and risks for", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 451, + 506, + 463 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 506, + 463 + ], + "score": 1.0, + "content": "many real-world applications like medicine, dialogue systems, or robotic control (Murphy et al., 2001;", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "Mandel et al., 2014; Gu et al., 2017a; Kalashnikov et al., 2018; Nachum et al., 2019; Jaques et al.,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 472, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 506, + 486 + ], + "score": 1.0, + "content": "2019). While there are abundant works on safety for RL (Chow et al., 2015; Eysenbach et al., 2018;", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 483, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 483, + 506, + 497 + ], + "score": 1.0, + "content": "Chow et al., 2018; Ray et al., 2019; Chow et al., 2019), they often do not provide guarantees in practice", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 496, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 505, + 507 + ], + "score": 1.0, + "content": "when combined with neural networks and stochastic optimization. It is therefore necessary to verify", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "each policy before deployment (e.g. measuring the variance of rewards or checking out-of-bounds", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 518, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 518, + 505, + 529 + ], + "score": 1.0, + "content": "actions). Due to such costs associated with each deployment, it is desirable to minimize the number", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 528, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 506, + 540 + ], + "score": 1.0, + "content": "of distinct deployments needed during the learning process. Even ignoring safety considerations,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 540, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 540, + 505, + 551 + ], + "score": 1.0, + "content": "frequent updates to a deployed policy can exacerbate communication bottlenecks in large-scale", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 549, + 506, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 506, + 562 + ], + "score": 1.0, + "content": "distributed RL systems, which are becoming more prevalent (Nair et al., 2015; Espeholt et al.,", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 560, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 506, + 574 + ], + "score": 1.0, + "content": "2018; 2019). We additionally discuss on the importance of the deployment efficiency in real-world", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 572, + 230, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 230, + 584 + ], + "score": 1.0, + "content": "applications. See Appendix C.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 589, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 588, + 507, + 602 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 507, + 602 + ], + "score": 1.0, + "content": "In order to focus research on these practical bottlenecks, we propose a novel measure of RL algorithms,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 600, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 505, + 613 + ], + "score": 1.0, + "content": "namely, deployment efficiency, which counts how many times the data-collection policy has been", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 611, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 106, + 611, + 505, + 624 + ], + "score": 1.0, + "content": "changed during improvement from random policy to solve the task. For example, if an RL algorithm", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 622, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 428, + 635 + ], + "score": 1.0, + "content": "operates by using its learned policy to collect transitions from the environment", + "type": "text" + }, + { + "bbox": [ + 428, + 622, + 435, + 632 + ], + "score": 0.65, + "content": "I", + "type": "inline_equation" + }, + { + "bbox": [ + 435, + 622, + 505, + 635 + ], + "score": 1.0, + "content": "times, each time", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 633, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 189, + 645 + ], + "score": 1.0, + "content": "collecting a batch of", + "type": "text" + }, + { + "bbox": [ + 190, + 633, + 199, + 643 + ], + "score": 0.8, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 633, + 403, + 645 + ], + "score": 1.0, + "content": "new transitions, then the number of deployments is", + "type": "text" + }, + { + "bbox": [ + 403, + 633, + 410, + 643 + ], + "score": 0.7, + "content": "I", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 633, + 506, + 645 + ], + "score": 1.0, + "content": ", while the total number", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 202, + 657 + ], + "score": 1.0, + "content": "of samples collected is", + "type": "text" + }, + { + "bbox": [ + 202, + 644, + 229, + 654 + ], + "score": 0.9, + "content": "I \\times B", + "type": "inline_equation" + }, + { + "bbox": [ + 230, + 643, + 278, + 657 + ], + "score": 1.0, + "content": ". The lower", + "type": "text" + }, + { + "bbox": [ + 279, + 644, + 285, + 654 + ], + "score": 0.73, + "content": "I", + "type": "inline_equation" + }, + { + "bbox": [ + 286, + 643, + 506, + 657 + ], + "score": 1.0, + "content": "is, the more deployment-efficient the algorithm is; in", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 253, + 668 + ], + "score": 1.0, + "content": "contrast, sample efficiency looks at", + "type": "text" + }, + { + "bbox": [ + 254, + 655, + 280, + 665 + ], + "score": 0.9, + "content": "I \\times B", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 654, + 506, + 668 + ], + "score": 1.0, + "content": ". Online RL algorithms, whether they are on-policy or", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 666, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 506, + 678 + ], + "score": 1.0, + "content": "off-policy, typically update the policy and acquire new transitions by deploying the newly updated", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 676, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 505, + 691 + ], + "score": 1.0, + "content": "policy at every iteration. This corresponds to performing hundreds to millions of deployments during", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "learning on standard benchmarks (Haarnoja et al., 2018), which is severely deployment inefficient.", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "On the other hand, offline RL literature only studies the case of 1 deployment. A deployment-efficient", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "algorithm would stand in the middle of these two extremes and ideally learn a successful policy from", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 721, + 417, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 417, + 732 + ], + "score": 1.0, + "content": "scratch while deploying only a few distinct policies, as illustrated in Figure 1.", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 47 + } + ], + "page_idx": 2, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 292, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "score": 1.0, + "content": "3", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 207, + 93 + ], + "lines": [ + { + "bbox": [ + 105, + 80, + 209, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 209, + 96 + ], + "score": 1.0, + "content": "2 PRELIMINARIES", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 106, + 505, + 206 + ], + "lines": [ + { + "bbox": [ + 106, + 106, + 505, + 119 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 475, + 119 + ], + "score": 1.0, + "content": "We consider a Markov Decision Process (MDP) setting, characterized by the tuple", + "type": "text" + }, + { + "bbox": [ + 475, + 107, + 505, + 118 + ], + "score": 0.84, + "content": "\\begin{array} { r l } { \\mathcal { M } } & { { } = } \\end{array}", + "type": "inline_equation" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 116, + 506, + 131 + ], + "spans": [ + { + "bbox": [ + 106, + 118, + 161, + 129 + ], + "score": 0.91, + "content": "( S , \\mathcal { A } , p , r , \\gamma )", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 116, + 194, + 131 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 194, + 118, + 203, + 128 + ], + "score": 0.79, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 116, + 281, + 131 + ], + "score": 1.0, + "content": "is the state space,", + "type": "text" + }, + { + "bbox": [ + 281, + 118, + 290, + 128 + ], + "score": 0.72, + "content": "\\mathcal { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 116, + 374, + 131 + ], + "score": 1.0, + "content": "is the action space,", + "type": "text" + }, + { + "bbox": [ + 374, + 118, + 413, + 129 + ], + "score": 0.92, + "content": "p ( s ^ { \\prime } | s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 413, + 116, + 506, + 131 + ], + "score": 1.0, + "content": "is the transition prob-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 128, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 237, + 141 + ], + "score": 1.0, + "content": "ability distribution or dynamics,", + "type": "text" + }, + { + "bbox": [ + 237, + 129, + 256, + 141 + ], + "score": 0.92, + "content": "r ( s )", + "type": "inline_equation" + }, + { + "bbox": [ + 256, + 128, + 364, + 141 + ], + "score": 1.0, + "content": "is the reward function and", + "type": "text" + }, + { + "bbox": [ + 364, + 129, + 405, + 141 + ], + "score": 0.91, + "content": "\\gamma \\in ( 0 , 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 128, + 506, + 141 + ], + "score": 1.0, + "content": "is the discount factor. A", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 138, + 507, + 153 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 133, + 153 + ], + "score": 1.0, + "content": "policy", + "type": "text" + }, + { + "bbox": [ + 133, + 142, + 141, + 150 + ], + "score": 0.71, + "content": "\\pi", + "type": "inline_equation" + }, + { + "bbox": [ + 141, + 138, + 507, + 153 + ], + "score": 1.0, + "content": "is a function that determines the agent behavior, mapping from states to probability distribu-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 150, + 506, + 164 + ], + "spans": [ + { + "bbox": [ + 106, + 150, + 342, + 164 + ], + "score": 1.0, + "content": "tions over actions. The goal is to obtain the optimal policy", + "type": "text" + }, + { + "bbox": [ + 343, + 151, + 354, + 160 + ], + "score": 0.86, + "content": "\\pi ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 150, + 506, + 164 + ], + "score": 1.0, + "content": ", which maximizes the expectation of", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 161, + 506, + 174 + ], + "spans": [ + { + "bbox": [ + 106, + 161, + 324, + 174 + ], + "score": 1.0, + "content": "discounted sum of rewards. The transition probability", + "type": "text" + }, + { + "bbox": [ + 325, + 162, + 363, + 173 + ], + "score": 0.93, + "content": "p ( s ^ { \\prime } | s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 161, + 506, + 174 + ], + "score": 1.0, + "content": "is usually unknown, and estimated", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 172, + 506, + 186 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 259, + 186 + ], + "score": 1.0, + "content": "with a parameterized dynamics model", + "type": "text" + }, + { + "bbox": [ + 260, + 173, + 271, + 185 + ], + "score": 0.87, + "content": "f _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 172, + 506, + 186 + ], + "score": 1.0, + "content": "(e.g. a neural network) in model-based RL. For simplicity,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 183, + 505, + 196 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 248, + 196 + ], + "score": 1.0, + "content": "we assume that the reward function", + "type": "text" + }, + { + "bbox": [ + 248, + 184, + 266, + 195 + ], + "score": 0.9, + "content": "r ( s )", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 183, + 505, + 196 + ], + "score": 1.0, + "content": "is known, and the reward can be computed for any arbitrary", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 194, + 483, + 207 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 483, + 207 + ], + "score": 1.0, + "content": "state, but we may extend to the unknown setting and predict it using a parameterized function.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 106, + 507, + 207 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 211, + 505, + 398 + ], + "lines": [ + { + "bbox": [ + 106, + 210, + 505, + 224 + ], + "spans": [ + { + "bbox": [ + 106, + 210, + 505, + 224 + ], + "score": 1.0, + "content": "On-policy vs Off-policy, Online vs Offline At a high-level, most RL algorithms alternate many", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 222, + 506, + 235 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 506, + 235 + ], + "score": 1.0, + "content": "times between collecting a batch of transitions (deployments) and optimizing the policy (learning).", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 232, + 506, + 246 + ], + "spans": [ + { + "bbox": [ + 105, + 232, + 506, + 246 + ], + "score": 1.0, + "content": "If the algorithms discard data after each policy update, they are on-policy (Schulman et al., 2015;", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 243, + 506, + 257 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 308, + 257 + ], + "score": 1.0, + "content": "2017), while if they accumulate data in a buffer", + "type": "text" + }, + { + "bbox": [ + 309, + 245, + 318, + 254 + ], + "score": 0.77, + "content": "\\mathcal { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 243, + 506, + 257 + ], + "score": 1.0, + "content": ", i.e. experience replay (Lin, 1992), they are", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 255, + 506, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 506, + 267 + ], + "score": 1.0, + "content": "off-policy (Mnih et al., 2015; Lillicrap et al., 2016; Gu et al., 2016; 2017b; Haarnoja et al., 2018;", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 266, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 505, + 277 + ], + "score": 1.0, + "content": "Fujimoto et al., 2019; Fakoor et al., 2019) because not all the data in buffer comes from the current", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 277, + 505, + 289 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 505, + 289 + ], + "score": 1.0, + "content": "policy. However, we consider all these algorithms to be online RL algorithms, since they involve", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 286, + 506, + 301 + ], + "spans": [ + { + "bbox": [ + 104, + 286, + 506, + 301 + ], + "score": 1.0, + "content": "many deployments during learning, ranging from hundreds to millions. On the other hand, in pure", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 299, + 507, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 507, + 311 + ], + "score": 1.0, + "content": "offline RL, one does not assume direct interaction and learns a policy from only a fixed dataset,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 309, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 505, + 323 + ], + "score": 1.0, + "content": "which effectively corresponds to a single deployment allowed for learning. Classically, interpolating", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 321, + 505, + 333 + ], + "spans": [ + { + "bbox": [ + 106, + 321, + 505, + 333 + ], + "score": 1.0, + "content": "these two extremes were semi-batch RL algorithms (Lange et al., 2012; Singh et al., 1995), which", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 331, + 504, + 344 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 428, + 344 + ], + "score": 1.0, + "content": "improve the policy through repetitions of collecting a large batch of transitions", + "type": "text" + }, + { + "bbox": [ + 428, + 332, + 504, + 344 + ], + "score": 0.94, + "content": "\\mathcal { D } = \\{ ( s , a , s ^ { \\prime } , r ) \\}", + "type": "inline_equation" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 343, + 505, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 505, + 356 + ], + "score": 1.0, + "content": "and performing many or full policy updates. While these semi-batch RL also realize good deployment", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 353, + 505, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 505, + 366 + ], + "score": 1.0, + "content": "efficiency, they have not been extensively studied with neural network function approximators or in", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 365, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 365, + 505, + 378 + ], + "score": 1.0, + "content": "off-policy settings with experience replay for scalable sample-efficient learning. In our work, we aim", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 375, + 505, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 505, + 389 + ], + "score": 1.0, + "content": "to have both high deployment efficiency and sample efficiency by developing an algorithm that can", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 386, + 422, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 422, + 399 + ], + "score": 1.0, + "content": "solve the tasks with minimal policy deployments as well as transition samples.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 18, + "bbox_fs": [ + 104, + 210, + 507, + 399 + ] + }, + { + "type": "title", + "bbox": [ + 109, + 415, + 262, + 428 + ], + "lines": [ + { + "bbox": [ + 105, + 414, + 264, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 414, + 264, + 430 + ], + "score": 1.0, + "content": "3 DEPLOYMENT EFFICIENCY", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 441, + 506, + 583 + ], + "lines": [ + { + "bbox": [ + 105, + 440, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 506, + 452 + ], + "score": 1.0, + "content": "Deploying a new policy for data collection can be associated with a number of costs and risks for", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 451, + 506, + 463 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 506, + 463 + ], + "score": 1.0, + "content": "many real-world applications like medicine, dialogue systems, or robotic control (Murphy et al., 2001;", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "Mandel et al., 2014; Gu et al., 2017a; Kalashnikov et al., 2018; Nachum et al., 2019; Jaques et al.,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 472, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 506, + 486 + ], + "score": 1.0, + "content": "2019). While there are abundant works on safety for RL (Chow et al., 2015; Eysenbach et al., 2018;", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 483, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 483, + 506, + 497 + ], + "score": 1.0, + "content": "Chow et al., 2018; Ray et al., 2019; Chow et al., 2019), they often do not provide guarantees in practice", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 496, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 505, + 507 + ], + "score": 1.0, + "content": "when combined with neural networks and stochastic optimization. It is therefore necessary to verify", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "each policy before deployment (e.g. measuring the variance of rewards or checking out-of-bounds", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 518, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 518, + 505, + 529 + ], + "score": 1.0, + "content": "actions). Due to such costs associated with each deployment, it is desirable to minimize the number", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 528, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 506, + 540 + ], + "score": 1.0, + "content": "of distinct deployments needed during the learning process. Even ignoring safety considerations,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 540, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 540, + 505, + 551 + ], + "score": 1.0, + "content": "frequent updates to a deployed policy can exacerbate communication bottlenecks in large-scale", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 549, + 506, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 506, + 562 + ], + "score": 1.0, + "content": "distributed RL systems, which are becoming more prevalent (Nair et al., 2015; Espeholt et al.,", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 560, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 506, + 574 + ], + "score": 1.0, + "content": "2018; 2019). We additionally discuss on the importance of the deployment efficiency in real-world", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 572, + 230, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 230, + 584 + ], + "score": 1.0, + "content": "applications. See Appendix C.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 440, + 506, + 584 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 589, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 588, + 507, + 602 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 507, + 602 + ], + "score": 1.0, + "content": "In order to focus research on these practical bottlenecks, we propose a novel measure of RL algorithms,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 600, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 505, + 613 + ], + "score": 1.0, + "content": "namely, deployment efficiency, which counts how many times the data-collection policy has been", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 611, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 106, + 611, + 505, + 624 + ], + "score": 1.0, + "content": "changed during improvement from random policy to solve the task. For example, if an RL algorithm", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 622, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 428, + 635 + ], + "score": 1.0, + "content": "operates by using its learned policy to collect transitions from the environment", + "type": "text" + }, + { + "bbox": [ + 428, + 622, + 435, + 632 + ], + "score": 0.65, + "content": "I", + "type": "inline_equation" + }, + { + "bbox": [ + 435, + 622, + 505, + 635 + ], + "score": 1.0, + "content": "times, each time", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 633, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 189, + 645 + ], + "score": 1.0, + "content": "collecting a batch of", + "type": "text" + }, + { + "bbox": [ + 190, + 633, + 199, + 643 + ], + "score": 0.8, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 633, + 403, + 645 + ], + "score": 1.0, + "content": "new transitions, then the number of deployments is", + "type": "text" + }, + { + "bbox": [ + 403, + 633, + 410, + 643 + ], + "score": 0.7, + "content": "I", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 633, + 506, + 645 + ], + "score": 1.0, + "content": ", while the total number", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 202, + 657 + ], + "score": 1.0, + "content": "of samples collected is", + "type": "text" + }, + { + "bbox": [ + 202, + 644, + 229, + 654 + ], + "score": 0.9, + "content": "I \\times B", + "type": "inline_equation" + }, + { + "bbox": [ + 230, + 643, + 278, + 657 + ], + "score": 1.0, + "content": ". The lower", + "type": "text" + }, + { + "bbox": [ + 279, + 644, + 285, + 654 + ], + "score": 0.73, + "content": "I", + "type": "inline_equation" + }, + { + "bbox": [ + 286, + 643, + 506, + 657 + ], + "score": 1.0, + "content": "is, the more deployment-efficient the algorithm is; in", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 253, + 668 + ], + "score": 1.0, + "content": "contrast, sample efficiency looks at", + "type": "text" + }, + { + "bbox": [ + 254, + 655, + 280, + 665 + ], + "score": 0.9, + "content": "I \\times B", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 654, + 506, + 668 + ], + "score": 1.0, + "content": ". Online RL algorithms, whether they are on-policy or", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 666, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 506, + 678 + ], + "score": 1.0, + "content": "off-policy, typically update the policy and acquire new transitions by deploying the newly updated", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 676, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 505, + 691 + ], + "score": 1.0, + "content": "policy at every iteration. This corresponds to performing hundreds to millions of deployments during", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "learning on standard benchmarks (Haarnoja et al., 2018), which is severely deployment inefficient.", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "On the other hand, offline RL literature only studies the case of 1 deployment. A deployment-efficient", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "algorithm would stand in the middle of these two extremes and ideally learn a successful policy from", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 721, + 417, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 417, + 732 + ], + "score": 1.0, + "content": "scratch while deploying only a few distinct policies, as illustrated in Figure 1.", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 47, + "bbox_fs": [ + 105, + 588, + 507, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 203 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "Recent deep RL literature seldom emphasizes deployment efficiency, with few exceptions in specific", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "score": 1.0, + "content": "applications (Kalashnikov et al., 2018) where such a learning procedure is necessary. Deployment-", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "inefficient algorithms will fail in scenarios where the deployment of each new policy is exorbitantly", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "score": 1.0, + "content": "expensive, such as safety-critical robotics or user-facing products. Although current state-of-the-art", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 505, + 138 + ], + "score": 1.0, + "content": "algorithms on continuous control have substantially improved sample or data efficiency, they have", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "score": 1.0, + "content": "not optimized for deployment efficiency. For example, SAC (Haarnoja et al., 2018), an efficient", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 147, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 147, + 505, + 161 + ], + "score": 1.0, + "content": "model-free off-policy algorithm, performs half a million to one million policy deployments during", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 158, + 506, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 506, + 172 + ], + "score": 1.0, + "content": "learning on MuJoCo (Todorov et al., 2012) benchmarks. ME-TRPO (Kurutach et al., 2018), a", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 171, + 504, + 182 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 504, + 182 + ], + "score": 1.0, + "content": "model-based algorithm, performs a much lower 100-300 policy deployments, although this is still", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 181, + 506, + 194 + ], + "spans": [ + { + "bbox": [ + 106, + 181, + 506, + 194 + ], + "score": 1.0, + "content": "relatively high for practical settings.2 In our work, we demonstrate successful learning on standard", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 192, + 326, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 192, + 326, + 204 + ], + "score": 1.0, + "content": "benchmark environments with only 5-10 deployments.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 5 + }, + { + "type": "title", + "bbox": [ + 107, + 219, + 364, + 233 + ], + "lines": [ + { + "bbox": [ + 105, + 219, + 365, + 234 + ], + "spans": [ + { + "bbox": [ + 105, + 219, + 365, + 234 + ], + "score": 1.0, + "content": "4 BEHAVIOR-REGULARIZED MODEL-ENSEMBLE", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 245, + 506, + 301 + ], + "lines": [ + { + "bbox": [ + 105, + 244, + 506, + 259 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 506, + 259 + ], + "score": 1.0, + "content": "To achieve a favorable combination of both high deployment and sample efficiency, we propose", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 255, + 506, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 506, + 270 + ], + "score": 1.0, + "content": "Behavior-Regularized Model-ENsemble (BREMEN). 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Each model", + "type": "text" + }, + { + "bbox": [ + 248, + 365, + 262, + 380 + ], + "score": 0.92, + "content": "\\hat { f } _ { \\phi _ { i } }", + "type": "inline_equation" + }, + { + "bbox": [ + 263, + 367, + 342, + 380 + ], + "score": 1.0, + "content": "is parameterized by", + "type": "text" + }, + { + "bbox": [ + 342, + 368, + 353, + 379 + ], + "score": 0.88, + "content": "\\phi _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 367, + 505, + 380 + ], + "score": 1.0, + "content": "and trained by the following objective,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 379, + 505, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 405, + 394 + ], + "score": 1.0, + "content": "which minimizes mean squared error between the prediction of next state", + "type": "text" + }, + { + "bbox": [ + 406, + 379, + 448, + 393 + ], + "score": 0.93, + "content": "\\hat { f } _ { \\phi _ { i } } \\left( s _ { t } , a _ { t } \\right)", + "type": "inline_equation" + }, + { + "bbox": [ + 449, + 379, + 505, + 394 + ], + "score": 1.0, + "content": "and true next", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 392, + 218, + 404 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 127, + 403 + ], + "score": 1.0, + "content": "state", + "type": "text" + }, + { + "bbox": [ + 127, + 394, + 146, + 404 + ], + "score": 0.89, + "content": "s _ { t + 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 393, + 205, + 403 + ], + "score": 1.0, + "content": "over a dataset", + "type": "text" + }, + { + "bbox": [ + 205, + 392, + 214, + 401 + ], + "score": 0.83, + "content": "\\mathcal { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 393, + 218, + 403 + ], + "score": 1.0, + "content": ":", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20 + }, + { + "type": "interline_equation", + "bbox": [ + 206, + 409, + 404, + 441 + ], + "lines": [ + { + "bbox": [ + 206, + 409, + 404, + 441 + ], + "spans": [ + { + "bbox": [ + 206, + 409, + 404, + 441 + ], + "score": 0.94, + "content": "\\operatorname* { m i n } _ { \\phi _ { i } } \\frac { 1 } { | \\mathcal { D } | } \\sum _ { \\left( s _ { t } , a _ { t } , s _ { t + 1 } \\right) \\in \\mathcal { D } } \\frac { 1 } { 2 } \\left. s _ { t + 1 } - 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To further bias the learned policy to be close to the data-collection", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 40 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 711, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 118, + 709, + 505, + 725 + ], + "spans": [ + { + "bbox": [ + 118, + 709, + 505, + 725 + ], + "score": 1.0, + "content": "2We examined the number of deployments by checking their original implementations, while the frequency", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 720, + 277, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 277, + 732 + ], + "score": 1.0, + "content": "of data collection is a tunable hyper-parameter.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 108, + 27, + 292, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 203 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "Recent deep RL literature seldom emphasizes deployment efficiency, with few exceptions in specific", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "score": 1.0, + "content": "applications (Kalashnikov et al., 2018) where such a learning procedure is necessary. 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Although current state-of-the-art", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 505, + 138 + ], + "score": 1.0, + "content": "algorithms on continuous control have substantially improved sample or data efficiency, they have", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "score": 1.0, + "content": "not optimized for deployment efficiency. For example, SAC (Haarnoja et al., 2018), an efficient", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 147, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 147, + 505, + 161 + ], + "score": 1.0, + "content": "model-free off-policy algorithm, performs half a million to one million policy deployments during", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 158, + 506, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 506, + 172 + ], + "score": 1.0, + "content": "learning on MuJoCo (Todorov et al., 2012) benchmarks. ME-TRPO (Kurutach et al., 2018), a", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 171, + 504, + 182 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 504, + 182 + ], + "score": 1.0, + "content": "model-based algorithm, performs a much lower 100-300 policy deployments, although this is still", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 181, + 506, + 194 + ], + "spans": [ + { + "bbox": [ + 106, + 181, + 506, + 194 + ], + "score": 1.0, + "content": "relatively high for practical settings.2 In our work, we demonstrate successful learning on standard", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 192, + 326, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 192, + 326, + 204 + ], + "score": 1.0, + "content": "benchmark environments with only 5-10 deployments.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 82, + 506, + 204 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 219, + 364, + 233 + ], + "lines": [ + { + "bbox": [ + 105, + 219, + 365, + 234 + ], + "spans": [ + { + "bbox": [ + 105, + 219, + 365, + 234 + ], + "score": 1.0, + "content": "4 BEHAVIOR-REGULARIZED MODEL-ENSEMBLE", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 245, + 506, + 301 + ], + "lines": [ + { + "bbox": [ + 105, + 244, + 506, + 259 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 506, + 259 + ], + "score": 1.0, + "content": "To achieve a favorable combination of both high deployment and sample efficiency, we propose", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 255, + 506, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 506, + 270 + ], + "score": 1.0, + "content": "Behavior-Regularized Model-ENsemble (BREMEN). BREMEN incorporates Dyna-style (Sutton,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 266, + 507, + 281 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 507, + 281 + ], + "score": 1.0, + "content": "1991; Kurutach et al., 2018) model-based RL, learning an ensemble of dynamics models in conjunc-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 277, + 505, + 292 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 505, + 292 + ], + "score": 1.0, + "content": "tion with a policy using imaginary rollouts and behavior regularization via conservative trust-region", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 289, + 143, + 302 + ], + "spans": [ + { + "bbox": [ + 106, + 289, + 143, + 302 + ], + "score": 1.0, + "content": "updates.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14, + "bbox_fs": [ + 105, + 244, + 507, + 302 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 314, + 338, + 326 + ], + "lines": [ + { + "bbox": [ + 105, + 315, + 339, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 339, + 327 + ], + "score": 1.0, + "content": "4.1 IMAGINARY ROLLOUT FROM MODEL ENSEMBLE", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 106, + 335, + 506, + 403 + ], + "lines": [ + { + "bbox": [ + 106, + 335, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 506, + 348 + ], + "score": 1.0, + "content": "As in recent Dyna-style model-based RL methods (Kurutach et al., 2018; Wang et al., 2019), BRE-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 346, + 506, + 367 + ], + "spans": [ + { + "bbox": [ + 104, + 346, + 214, + 365 + ], + "score": 1.0, + "content": "MEN uses an ensemble of", + "type": "text" + }, + { + "bbox": [ + 214, + 351, + 224, + 360 + ], + "score": 0.8, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 225, + 346, + 352, + 365 + ], + "score": 1.0, + "content": "deterministic dynamics models", + "type": "text" + }, + { + "bbox": [ + 352, + 347, + 443, + 367 + ], + "score": 0.93, + "content": "\\hat { f } _ { \\phi } = \\left\\{ \\hat { f } _ { \\phi _ { 1 } } , \\dots , \\hat { f } _ { \\phi _ { K } } \\right\\}", + "type": "inline_equation" + }, + { + "bbox": [ + 443, + 346, + 506, + 365 + ], + "score": 1.0, + "content": "to alleviate the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 365, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 106, + 367, + 248, + 380 + ], + "score": 1.0, + "content": "problem of model bias. Each model", + "type": "text" + }, + { + "bbox": [ + 248, + 365, + 262, + 380 + ], + "score": 0.92, + "content": "\\hat { f } _ { \\phi _ { i } }", + "type": "inline_equation" + }, + { + "bbox": [ + 263, + 367, + 342, + 380 + ], + "score": 1.0, + "content": "is parameterized by", + "type": "text" + }, + { + "bbox": [ + 342, + 368, + 353, + 379 + ], + "score": 0.88, + "content": "\\phi _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 367, + 505, + 380 + ], + "score": 1.0, + "content": "and trained by the following objective,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 379, + 505, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 405, + 394 + ], + "score": 1.0, + "content": "which minimizes mean squared error between the prediction of next state", + "type": "text" + }, + { + "bbox": [ + 406, + 379, + 448, + 393 + ], + "score": 0.93, + "content": "\\hat { f } _ { \\phi _ { i } } \\left( s _ { t } , a _ { t } \\right)", + "type": "inline_equation" + }, + { + "bbox": [ + 449, + 379, + 505, + 394 + ], + "score": 1.0, + "content": "and true next", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 392, + 218, + 404 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 127, + 403 + ], + "score": 1.0, + "content": "state", + "type": "text" + }, + { + "bbox": [ + 127, + 394, + 146, + 404 + ], + "score": 0.89, + "content": "s _ { t + 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 393, + 205, + 403 + ], + "score": 1.0, + "content": "over a dataset", + "type": "text" + }, + { + "bbox": [ + 205, + 392, + 214, + 401 + ], + "score": 0.83, + "content": "\\mathcal { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 393, + 218, + 403 + ], + "score": 1.0, + "content": ":", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20, + "bbox_fs": [ + 104, + 335, + 506, + 404 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 206, + 409, + 404, + 441 + ], + "lines": [ + { + "bbox": [ + 206, + 409, + 404, + 441 + ], + "spans": [ + { + "bbox": [ + 206, + 409, + 404, + 441 + ], + "score": 0.94, + "content": "\\operatorname* { m i n } _ { \\phi _ { i } } \\frac { 1 } { | \\mathcal { D } | } \\sum _ { \\left( s _ { t } , a _ { t } , s _ { t + 1 } \\right) \\in \\mathcal { D } } \\frac { 1 } { 2 } \\left. s _ { t + 1 } - 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To further bias the learned policy to be close to the data-collection", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 645, + 505, + 703 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 82, + 306, + 94 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 307, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 307, + 95 + ], + "score": 1.0, + "content": "Algorithm 1 BREMEN for Deployment-Efficient RL", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 108, + 97, + 504, + 223 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 108, + 97, + 504, + 223 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 97, + 504, + 223 + ], + "spans": [ + { + "bbox": [ + 108, + 97, + 504, + 223 + ], + "score": 0.943, + "html": "
Input: Empty dataset Dau,D,Initial parameters Φ = {1,·,Φk},β,Number of policy optimization T
Numberof deploymentsI.
1:Randomly initialize the target policy πθ .
2:for deploymenti=1,·.,I do
3:Collect B transitions in the true environment using T and add them to dataset
Dall←DalU{St,at,rt,St+1},D←{st,at,rt,St+1}.
4:Train K dynamics models f using Dau via Equation 1.
5: 6:Train estimated behavior policy πβ using D by behavior cloning via Equation 3.
7:Re-initialize target policy πeo = Normal(β,1). for policy optimization k =1,..·,T do
8:Generate imaginary rollout via Equation 2.
9:Optimize target policy Tβ satisfying Equation 4 with the rollout.
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Therefore, the", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 256, + 252, + 269 + ], + "spans": [ + { + "bbox": [ + 106, + 256, + 252, + 269 + ], + "score": 1.0, + "content": "optimization of BREMEN becomes", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4.5 + }, + { + "type": "interline_equation", + "bbox": [ + 152, + 273, + 457, + 327 + ], + "lines": [ + { + "bbox": [ + 152, + 273, + 457, + 327 + ], + "spans": [ + { + "bbox": [ + 152, + 273, + 457, + 327 + ], + "score": 0.94, + "content": "\\begin{array} { r l } & { \\theta _ { k + 1 } = \\underset { \\theta } { \\arg \\operatorname* { m a x } } \\ \\underset { s , a \\sim \\pi _ { \\theta _ { k } } , \\hat { f } _ { \\phi _ { i } } } { \\mathbb { E } } [ \\frac { \\pi _ { \\theta } ( a | s ) } { \\pi _ { \\theta _ { k } } ( a | s ) } A ^ { \\pi _ { \\theta _ { k } } } ( s , a ) ] } \\\\ & { \\mathrm { s . t . } \\quad \\underset { s \\sim \\pi _ { \\theta _ { k } } , \\hat { f } _ { \\phi _ { i } } } { \\mathbb { E } } [ D _ { \\mathrm { K L } } ( \\pi _ { \\theta } ( \\cdot | s ) | | \\pi _ { \\theta _ { k } } ( \\cdot | s ) ) ] \\leq \\delta , \\quad \\pi _ { \\theta _ { 0 } } = \\mathrm { N o r m a l } ( \\hat { \\pi } _ { \\beta } , 1 ) , } \\end{array}", + "type": "interline_equation", + "image_path": "8af682036a9c8970146000e325dfec08320cd1c07d20dafde4f6238f0d1bf694.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 152, + 273, + 457, + 291.0 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 152, + 291.0, + 457, + 309.0 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 152, + 309.0, + 457, + 327.0 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 333, + 504, + 357 + ], + "lines": [ + { + "bbox": [ + 105, + 332, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 332, + 135, + 347 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 135, + 334, + 179, + 345 + ], + "score": 0.93, + "content": "A ^ { \\pi _ { \\theta _ { k } } } ( s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 179, + 332, + 265, + 347 + ], + "score": 1.0, + "content": "is the advantage of", + "type": "text" + }, + { + "bbox": [ + 266, + 336, + 281, + 346 + ], + "score": 0.88, + "content": "\\pi _ { \\theta _ { k } }", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 332, + 505, + 347 + ], + "score": 1.0, + "content": "computed using model-based rollouts in the learned", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 344, + 305, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 191, + 357 + ], + "score": 1.0, + "content": "dynamics model and", + "type": "text" + }, + { + "bbox": [ + 192, + 345, + 198, + 355 + ], + "score": 0.79, + "content": "\\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 198, + 344, + 305, + 357 + ], + "score": 1.0, + "content": "is the maximum step size.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 107, + 361, + 505, + 428 + ], + "lines": [ + { + "bbox": [ + 105, + 361, + 506, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 506, + 374 + ], + "score": 1.0, + "content": "The combination of BC for initialization and finite iterative trust-region updates serves as an implicit", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 372, + 505, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 505, + 385 + ], + "score": 1.0, + "content": "KL regularization. This is in contrast to many previous offline RL algorithms that augment the value", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "score": 1.0, + "content": "function with a penalty of explicit KL divergence (Siegel et al., 2020; Wu et al., 2019) or maximum", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 394, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 106, + 394, + 505, + 407 + ], + "score": 1.0, + "content": "mean discrepancy (Kumar et al., 2019). Empirically, we found that our regularization technique", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 406, + 505, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 505, + 418 + ], + "score": 1.0, + "content": "outperforms the explicit KL penalty (Section 5.3). Furthermore, we provide a mathematical intuition", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 416, + 506, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 416, + 506, + 429 + ], + "score": 1.0, + "content": "explaining how our methods works as an implicit regularization of distributional shift in Appendix A.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 107, + 433, + 505, + 467 + ], + "lines": [ + { + "bbox": [ + 105, + 432, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 505, + 448 + ], + "score": 1.0, + "content": "By recursively performing offline procedure, BREMEN can be used for deployment-efficient learning", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 444, + 504, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 504, + 456 + ], + "score": 1.0, + "content": "as shown in Algorithm 1, starting from a randomly initialized policy, collecting experience data, and", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 456, + 244, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 244, + 468 + ], + "score": 1.0, + "content": "performing offline policy updates.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18 + }, + { + "type": "title", + "bbox": [ + 108, + 484, + 200, + 496 + ], + "lines": [ + { + "bbox": [ + 105, + 483, + 201, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 201, + 498 + ], + "score": 1.0, + "content": "5 EXPERIMENTS", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 106, + 509, + 505, + 608 + ], + "lines": [ + { + "bbox": [ + 106, + 508, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 505, + 522 + ], + "score": 1.0, + "content": "In order to realize a deployment-efficient RL algorithm, the batch policy optimizer has to be stable", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 520, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 505, + 533 + ], + "score": 1.0, + "content": "and sample-efficient. We first evaluate BREMEN in the offline setting, where the algorithm learns", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 531, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 488, + 543 + ], + "score": 1.0, + "content": "the policy from a static dataset. Standard benchmarks of MuJoCo physics simulator shown in", + "type": "text" + }, + { + "bbox": [ + 489, + 532, + 505, + 542 + ], + "score": 0.38, + "content": "\\mathrm { W u }", + "type": "inline_equation" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 542, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 506, + 554 + ], + "score": 1.0, + "content": "et al., 2019) and more recent datasets (Fu et al., 2020) are used in the evaluation, and we compared", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 553, + 506, + 566 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 506, + 566 + ], + "score": 1.0, + "content": "the asymptotic performance of BREMEN with other offline RL methods including the concurrent", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 564, + 506, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 506, + 577 + ], + "score": 1.0, + "content": "model-based approaches. We then tested the sample-efficiency of offline algorithms using smaller", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 575, + 504, + 587 + ], + "spans": [ + { + "bbox": [ + 106, + 575, + 504, + 587 + ], + "score": 1.0, + "content": "datasets. We lastly extend the experiment to deployment-efficient settings, where the algorithms learn", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 585, + 506, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 506, + 599 + ], + "score": 1.0, + "content": "their policies from scratch via a limited number of deployments and perform some ablations to see", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 597, + 453, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 597, + 453, + 609 + ], + "score": 1.0, + "content": "how components in BREMEN affect performance. See Appendix F for further details.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 25 + }, + { + "type": "title", + "bbox": [ + 107, + 622, + 316, + 634 + ], + "lines": [ + { + "bbox": [ + 106, + 622, + 317, + 635 + ], + "spans": [ + { + "bbox": [ + 106, + 622, + 317, + 635 + ], + "score": 1.0, + "content": "5.1 EVALUATING OFFLINE RL PERFORMANCES", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 643, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 643, + 505, + 656 + ], + "score": 1.0, + "content": "Standard Benchmarks We evaluate BREMEN on standard offline RL benchmarks following and", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "score": 1.0, + "content": "identical protocol as in Wu et al. (2019): We first train online SAC to a certain cumulative reward", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "threshold, 4,000 in HalfCheetah, 1,000 in Ant, Hopper, and Walker2d, and collect offline datasets. We", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "evaluate agents with the offline dataset of one million (1M) transitions, which is standard for BCQ and", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "BRAC. Table 1 (top) shows that BREMEN can achieve performance competitive with state-of-the-art", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 698, + 505, + 710 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 710 + ], + "score": 1.0, + "content": "model-free offline RL algorithms when using the standard dataset size of 1M. We also test BREMEN", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "score": 1.0, + "content": "with more recent benchmarks of D4RL (Fu et al., 2020) and compared the performance with the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 720, + 424, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 424, + 732 + ], + "score": 1.0, + "content": "existing model-free and model-based methods. See Appendix D for the results.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 34.5 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 292, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 82, + 306, + 94 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 307, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 307, + 95 + ], + "score": 1.0, + "content": "Algorithm 1 BREMEN for Deployment-Efficient RL", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 108, + 97, + 504, + 223 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 108, + 97, + 504, + 223 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 97, + 504, + 223 + ], + "spans": [ + { + "bbox": [ + 108, + 97, + 504, + 223 + ], + "score": 0.943, + "html": "
Input: Empty dataset Dau,D,Initial parameters Φ = {1,·,Φk},β,Number of policy optimization T
Numberof deploymentsI.
1:Randomly initialize the target policy πθ .
2:for deploymenti=1,·.,I do
3:Collect B transitions in the true environment using T and add them to dataset
Dall←DalU{St,at,rt,St+1},D←{st,at,rt,St+1}.
4:Train K dynamics models f using Dau via Equation 1.
5: 6:Train estimated behavior policy πβ using D by behavior cloning via Equation 3.
7:Re-initialize target policy πeo = Normal(β,1). for policy optimization k =1,..·,T do
8:Generate imaginary rollout via Equation 2.
9:Optimize target policy Tβ satisfying Equation 4 with the rollout.
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Therefore, the", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 256, + 252, + 269 + ], + "spans": [ + { + "bbox": [ + 106, + 256, + 252, + 269 + ], + "score": 1.0, + "content": "optimization of BREMEN becomes", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4.5, + "bbox_fs": [ + 105, + 244, + 505, + 269 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 152, + 273, + 457, + 327 + ], + "lines": [ + { + "bbox": [ + 152, + 273, + 457, + 327 + ], + "spans": [ + { + "bbox": [ + 152, + 273, + 457, + 327 + ], + "score": 0.94, + "content": "\\begin{array} { r l } & { \\theta _ { k + 1 } = \\underset { \\theta } { \\arg \\operatorname* { m a x } } \\ \\underset { s , a \\sim \\pi _ { \\theta _ { k } } , \\hat { f } _ { \\phi _ { i } } } { \\mathbb { E } } [ \\frac { \\pi _ { \\theta } ( a | s ) } { \\pi _ { \\theta _ { k } } ( a | s ) } A ^ { \\pi _ { \\theta _ { k } } } ( s , a ) ] } \\\\ & { \\mathrm { s . t . } \\quad \\underset { s \\sim \\pi _ { \\theta _ { k } } , \\hat { f } _ { \\phi _ { i } } } { \\mathbb { E } } [ D _ { \\mathrm { K L } } ( \\pi _ { \\theta } ( \\cdot | s ) | | \\pi _ { \\theta _ { k } } ( \\cdot | s ) ) ] \\leq \\delta , \\quad \\pi _ { \\theta _ { 0 } } = \\mathrm { N o r m a l } ( \\hat { \\pi } _ { \\beta } , 1 ) , } \\end{array}", + "type": "interline_equation", + "image_path": "8af682036a9c8970146000e325dfec08320cd1c07d20dafde4f6238f0d1bf694.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 152, + 273, + 457, + 291.0 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 152, + 291.0, + 457, + 309.0 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 152, + 309.0, + 457, + 327.0 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 333, + 504, + 357 + ], + "lines": [ + { + "bbox": [ + 105, + 332, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 332, + 135, + 347 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 135, + 334, + 179, + 345 + ], + "score": 0.93, + "content": "A ^ { \\pi _ { \\theta _ { k } } } ( s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 179, + 332, + 265, + 347 + ], + "score": 1.0, + "content": "is the advantage of", + "type": "text" + }, + { + "bbox": [ + 266, + 336, + 281, + 346 + ], + "score": 0.88, + "content": "\\pi _ { \\theta _ { k } }", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 332, + 505, + 347 + ], + "score": 1.0, + "content": "computed using model-based rollouts in the learned", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 344, + 305, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 191, + 357 + ], + "score": 1.0, + "content": "dynamics model and", + "type": "text" + }, + { + "bbox": [ + 192, + 345, + 198, + 355 + ], + "score": 0.79, + "content": "\\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 198, + 344, + 305, + 357 + ], + "score": 1.0, + "content": "is the maximum step size.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9.5, + "bbox_fs": [ + 105, + 332, + 505, + 357 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 361, + 505, + 428 + ], + "lines": [ + { + "bbox": [ + 105, + 361, + 506, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 506, + 374 + ], + "score": 1.0, + "content": "The combination of BC for initialization and finite iterative trust-region updates serves as an implicit", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 372, + 505, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 505, + 385 + ], + "score": 1.0, + "content": "KL regularization. This is in contrast to many previous offline RL algorithms that augment the value", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "score": 1.0, + "content": "function with a penalty of explicit KL divergence (Siegel et al., 2020; Wu et al., 2019) or maximum", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 394, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 106, + 394, + 505, + 407 + ], + "score": 1.0, + "content": "mean discrepancy (Kumar et al., 2019). Empirically, we found that our regularization technique", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 406, + 505, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 505, + 418 + ], + "score": 1.0, + "content": "outperforms the explicit KL penalty (Section 5.3). Furthermore, we provide a mathematical intuition", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 416, + 506, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 416, + 506, + 429 + ], + "score": 1.0, + "content": "explaining how our methods works as an implicit regularization of distributional shift in Appendix A.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 361, + 506, + 429 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 433, + 505, + 467 + ], + "lines": [ + { + "bbox": [ + 105, + 432, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 505, + 448 + ], + "score": 1.0, + "content": "By recursively performing offline procedure, BREMEN can be used for deployment-efficient learning", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 444, + 504, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 504, + 456 + ], + "score": 1.0, + "content": "as shown in Algorithm 1, starting from a randomly initialized policy, collecting experience data, and", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 456, + 244, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 244, + 468 + ], + "score": 1.0, + "content": "performing offline policy updates.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 432, + 505, + 468 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 484, + 200, + 496 + ], + "lines": [ + { + "bbox": [ + 105, + 483, + 201, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 201, + 498 + ], + "score": 1.0, + "content": "5 EXPERIMENTS", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 106, + 509, + 505, + 608 + ], + "lines": [ + { + "bbox": [ + 106, + 508, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 505, + 522 + ], + "score": 1.0, + "content": "In order to realize a deployment-efficient RL algorithm, the batch policy optimizer has to be stable", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 520, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 505, + 533 + ], + "score": 1.0, + "content": "and sample-efficient. We first evaluate BREMEN in the offline setting, where the algorithm learns", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 531, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 488, + 543 + ], + "score": 1.0, + "content": "the policy from a static dataset. Standard benchmarks of MuJoCo physics simulator shown in", + "type": "text" + }, + { + "bbox": [ + 489, + 532, + 505, + 542 + ], + "score": 0.38, + "content": "\\mathrm { W u }", + "type": "inline_equation" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 542, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 506, + 554 + ], + "score": 1.0, + "content": "et al., 2019) and more recent datasets (Fu et al., 2020) are used in the evaluation, and we compared", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 553, + 506, + 566 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 506, + 566 + ], + "score": 1.0, + "content": "the asymptotic performance of BREMEN with other offline RL methods including the concurrent", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 564, + 506, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 506, + 577 + ], + "score": 1.0, + "content": "model-based approaches. We then tested the sample-efficiency of offline algorithms using smaller", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 575, + 504, + 587 + ], + "spans": [ + { + "bbox": [ + 106, + 575, + 504, + 587 + ], + "score": 1.0, + "content": "datasets. We lastly extend the experiment to deployment-efficient settings, where the algorithms learn", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 585, + 506, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 506, + 599 + ], + "score": 1.0, + "content": "their policies from scratch via a limited number of deployments and perform some ablations to see", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 597, + 453, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 597, + 453, + 609 + ], + "score": 1.0, + "content": "how components in BREMEN affect performance. See Appendix F for further details.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 25, + "bbox_fs": [ + 105, + 508, + 506, + 609 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 622, + 316, + 634 + ], + "lines": [ + { + "bbox": [ + 106, + 622, + 317, + 635 + ], + "spans": [ + { + "bbox": [ + 106, + 622, + 317, + 635 + ], + "score": 1.0, + "content": "5.1 EVALUATING OFFLINE RL PERFORMANCES", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 643, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 643, + 505, + 656 + ], + "score": 1.0, + "content": "Standard Benchmarks We evaluate BREMEN on standard offline RL benchmarks following and", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "score": 1.0, + "content": "identical protocol as in Wu et al. (2019): We first train online SAC to a certain cumulative reward", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "threshold, 4,000 in HalfCheetah, 1,000 in Ant, Hopper, and Walker2d, and collect offline datasets. We", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "evaluate agents with the offline dataset of one million (1M) transitions, which is standard for BCQ and", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "BRAC. Table 1 (top) shows that BREMEN can achieve performance competitive with state-of-the-art", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 698, + 505, + 710 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 710 + ], + "score": 1.0, + "content": "model-free offline RL algorithms when using the standard dataset size of 1M. We also test BREMEN", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "score": 1.0, + "content": "with more recent benchmarks of D4RL (Fu et al., 2020) and compared the performance with the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 720, + 424, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 424, + 732 + ], + "score": 1.0, + "content": "existing model-free and model-based methods. See Appendix D for the results.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 34.5, + "bbox_fs": [ + 105, + 643, + 506, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 153, + 82, + 457, + 357 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 153, + 82, + 457, + 357 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 153, + 82, + 457, + 357 + ], + "spans": [ + { + "bbox": [ + 153, + 82, + 457, + 357 + ], + "score": 0.935, + "html": "
1,000,000(1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset BC1191 1321±141412611281376
4281±12 5783±2721341±161 1130±1271421±147 2153±753
BCQ2021±31 2072±2851422±90
BRAC7192±1152239±1124
BRAC (max Q)2369±2347320±911916±3432409±1210
BREMEN (Ours)3328±2758055±1032058±8522346±230
ME-TRPO (offline)1258±5501804±924518±91211±154
100,000(100K)transitions
MethodAntHalfCheetahHopperWalker2d
Dataset1191406611281376
BC1330±814266±211322±1091426±47
BCQ1363±1993915±4111129±2382187±196
BRAC-157±3832505±25011310±702162±1109
BRAC (max Q)-226±3872332±24221422±1012164±1114
BREMEN (Ours)1633±1276095±3702191±4552132±301
ME-TRPO (offline)974±42±434307±17010±61
50,000 (50K) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset1191413811281376
BC1270±654230±491249±611420±194
BCQ1329±951319±6261178±2351841±439
BRAC-878±244-597±731277±102976±1207
BRAC (max Q)-843±279-590±561276±225903±1137
BREMEN(Ours)1347±2835823±1461632±7962280±647
938±32
ME-TRPO (offfline)-73±95152±13176±343
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Each cell shows the average", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 369, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 506, + 383 + ], + "score": 1.0, + "content": "cumulative reward and their standard deviation, where the number of samples is 1M, 100K, and 50K, respectively.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 381, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 106, + 381, + 505, + 393 + ], + "score": 1.0, + "content": "The maximum steps per episode is 1,000. BRAC applies a primal form of KL value penalty, and BRAC (max Q)", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 391, + 497, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 391, + 497, + 403 + ], + "score": 1.0, + "content": "means its variant of sampling multiple actions and taking the maximum according to the learned Q function.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23.5 + } + ], + "index": 17.0 + }, + { + "type": "text", + "bbox": [ + 107, + 423, + 505, + 489 + ], + "lines": [ + { + "bbox": [ + 106, + 424, + 505, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 505, + 435 + ], + "score": 1.0, + "content": "Evaluating Sample-Efficiency We then evaluate the sample-efficiency by making much smaller", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 434, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 150, + 447 + ], + "score": 1.0, + "content": "datasets of", + "type": "text" + }, + { + "bbox": [ + 150, + 435, + 167, + 445 + ], + "score": 0.53, + "content": "5 0 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 167, + 434, + 185, + 447 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 185, + 435, + 205, + 445 + ], + "score": 0.35, + "content": "1 0 0 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 206, + 434, + 252, + 447 + ], + "score": 1.0, + "content": "transitions", + "type": "text" + }, + { + "bbox": [ + 252, + 435, + 287, + 445 + ], + "score": 0.89, + "content": "5 \\sim 1 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 288, + 434, + 505, + 447 + ], + "score": 1.0, + "content": "of Wu et al. (2019)). Surprisingly, Table 1 (middle and", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 446, + 504, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 446, + 504, + 457 + ], + "score": 1.0, + "content": "bottom) shows that BREMEN can also learn with smaller datasets, where BCQ and BRAC are unable", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 457, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 106, + 457, + 505, + 468 + ], + "score": 1.0, + "content": "to exceed even BC baseline. This is a novel evaluation protocol we proposed, and our BREMEN’s", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 467, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 505, + 479 + ], + "score": 1.0, + "content": "superior performance here is exactly what enables recursive BREMEN in the next section to be an", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 478, + 329, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 329, + 492 + ], + "score": 1.0, + "content": "effective algorithm in deployment-constrained settings.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28.5 + }, + { + "type": "title", + "bbox": [ + 107, + 503, + 432, + 515 + ], + "lines": [ + { + "bbox": [ + 105, + 502, + 434, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 434, + 516 + ], + "score": 1.0, + "content": "5.2 EVALUATING DEPLOYMENT EFFICIENCY IN ONLINE RL BENCHMARKS", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 107, + 524, + 505, + 591 + ], + "lines": [ + { + "bbox": [ + 106, + 525, + 506, + 536 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 506, + 536 + ], + "score": 1.0, + "content": "We compare BREMEN to ME-TRPO, SAC, BCQ, and BRAC applied to limited deployment settings.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 534, + 504, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 534, + 504, + 548 + ], + "score": 1.0, + "content": "To adapt offline methods (BCQ, BRAC) to this setting, we simply apply them in a recursive fashion;3", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 546, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 546, + 505, + 559 + ], + "score": 1.0, + "content": "at each deployment iteration, we collect a batch of data with the most recent policy and then run the", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 556, + 506, + 570 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 506, + 570 + ], + "score": 1.0, + "content": "offline update with this dataset. 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1,000,000(1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset BC1191 1321±141412611281376
4281±12 5783±2721341±161 1130±1271421±147 2153±753
BCQ2021±31 2072±2851422±90
BRAC7192±1152239±1124
BRAC (max Q)2369±2347320±911916±3432409±1210
BREMEN (Ours)3328±2758055±1032058±8522346±230
ME-TRPO (offline)1258±5501804±924518±91211±154
100,000(100K)transitions
MethodAntHalfCheetahHopperWalker2d
Dataset1191406611281376
BC1330±814266±211322±1091426±47
BCQ1363±1993915±4111129±2382187±196
BRAC-157±3832505±25011310±702162±1109
BRAC (max Q)-226±3872332±24221422±1012164±1114
BREMEN (Ours)1633±1276095±3702191±4552132±301
ME-TRPO (offline)974±42±434307±17010±61
50,000 (50K) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset1191413811281376
BC1270±654230±491249±611420±194
BCQ1329±951319±6261178±2351841±439
BRAC-878±244-597±731277±102976±1207
BRAC (max Q)-843±279-590±561276±225903±1137
BREMEN(Ours)1347±2835823±1461632±7962280±647
938±32
ME-TRPO (offfline)-73±95152±13176±343
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As a point", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 629, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 106, + 629, + 505, + 641 + ], + "score": 1.0, + "content": "of comparison, we also include results for online SAC and ME-TRPO without deployment-limits but", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 640, + 506, + 652 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 506, + 652 + ], + "score": 1.0, + "content": "using the same number of transitions. We additionally compare BREMEN to the model-based offline", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 651, + 434, + 664 + ], + "spans": [ + { + "bbox": [ + 105, + 651, + 434, + 664 + ], + "score": 1.0, + "content": "RL methods with uncertainty-based penalties. See Appendix E for further details.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 596, + 506, + 664 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 668, + 504, + 702 + ], + "lines": [ + { + "bbox": [ + 106, + 668, + 505, + 681 + ], + "spans": [ + { + "bbox": [ + 106, + 668, + 505, + 681 + ], + "score": 1.0, + "content": "Following the motivation of deployment efficiency, obtaining a successful policy under data-collection", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 679, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 679, + 505, + 691 + ], + "score": 1.0, + "content": "constraint conditions in the real application, we extensively evaluate our algorithm on more realistic", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 690, + 505, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 690, + 505, + 702 + ], + "score": 1.0, + "content": "robotics environments in OpenAI Gym. The experimental procedure is the same as above, while", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 530, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 530, + 314, + 543 + ], + "score": 1.0, + "content": "we limit the batch size at each deployment as only", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 314, + 531, + 331, + 541 + ], + "score": 0.68, + "content": "2 5 \\mathrm { k }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 331, + 530, + 505, + 543 + ], + "score": 1.0, + "content": ". Figure 3 presents the reaching tasks with", + "type": "text", + "cross_page": true + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 540, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 505, + 554 + ], + "score": 1.0, + "content": "Fetch robot and 20-DoF shadow hand (Plappert et al., 2018), and the experimental results in both", + "type": "text", + "cross_page": true + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 552, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 505, + 565 + ], + "score": 1.0, + "content": "environments. Only BREMEN shows stable improvement and high performance, while other offline", + "type": "text", + "cross_page": true + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 563, + 506, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 506, + 576 + ], + "score": 1.0, + "content": "and online algorithms fail to learn. These results suggest that a model-based method is a desirable", + "type": "text", + "cross_page": true + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 574, + 495, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 495, + 587 + ], + "score": 1.0, + "content": "approach for satisfying practical requirements in robotics, i.e. sample and deployment efficiency.", + "type": "text", + "cross_page": true + } + ], + "index": 27 + } + ], + "index": 46, + "bbox_fs": [ + 106, + 668, + 505, + 702 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 120, + 81, + 493, + 209 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 120, + 81, + 493, + 209 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 120, + 81, + 493, + 209 + ], + "spans": [ + { + "bbox": [ + 120, + 81, + 493, + 209 + ], + "score": 0.968, + "type": "image", + "image_path": "6a1cb8fc593fa991de860c81499864a36dc243a21b814426030744b691e27217.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 120, + 81, + 493, + 123.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 120, + 123.66666666666666, + 493, + 166.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 120, + 166.33333333333331, + 493, + 208.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 213, + 506, + 353 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 213, + 506, + 225 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 506, + 225 + ], + "score": 1.0, + "content": "Figure 2: Evaluation of BREMEN with the existing methods (ME-TRPO, SAC, BCQ, BRAC) under deployment", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 223, + 506, + 235 + ], + "spans": [ + { + "bbox": [ + 104, + 223, + 506, + 235 + ], + "score": 1.0, + "content": "constraints (to 5-10 deployments with batch sizes of 200k and 100k). The average cumulative rewards and their", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 234, + 506, + 245 + ], + "spans": [ + { + "bbox": [ + 106, + 234, + 506, + 245 + ], + "score": 1.0, + "content": "standard deviations with 5 random seeds are shown. Vertical dotted lines represent where each policy deployment", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 243, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 506, + 255 + ], + "score": 1.0, + "content": "and data collection happen. BREMEN is able to learn successful policies with only 5-10 deployments, while the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 254, + 506, + 265 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 506, + 265 + ], + "score": 1.0, + "content": "state-of-the-art off-policy (SAC), model-based (ME-TRPO), and recursively-applied offline RL algorithms (BCQ,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 263, + 506, + 276 + ], + "spans": [ + { + "bbox": [ + 105, + 263, + 506, + 276 + ], + "score": 1.0, + "content": "BRAC) often struggle to make any progress. For completeness, we show ME-TRPO(online) and SAC(online)", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 273, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 506, + 285 + ], + "score": 1.0, + "content": "which are their original optimal learning curves without deployment constraints, plotted with respect to samples", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "score": 1.0, + "content": "normalized by the batch size. While SAC(online) substantially outperforms BREMEN in sample efficiency, it", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 293, + 506, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 506, + 305 + ], + "score": 1.0, + "content": "uses 1 deployment per sample, leading to 100k-500k deployments required for learning. Interestingly, BREMEN", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 302, + 506, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 506, + 315 + ], + "score": 1.0, + "content": "achieves even better performance than the original ME-TRPO(online), suggesting the effectiveness of implicit", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 312, + 505, + 325 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 505, + 325 + ], + "score": 1.0, + "content": "behavior regularization. For SAC and ME-TRPO under deployment-constrained evaluation, their batch size", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 323, + 505, + 334 + ], + "spans": [ + { + "bbox": [ + 106, + 323, + 505, + 334 + ], + "score": 1.0, + "content": "between policy deployments differs substantially from their standard settings, and therefore we performed", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 333, + 506, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 506, + 346 + ], + "score": 1.0, + "content": "extensive hyper-parameter search on the relevant parameters such as the number of policy updates between", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 343, + 272, + 354 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 272, + 354 + ], + "score": 1.0, + "content": "deployments, as discussed in Appendix F.2.1.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 9.5 + } + ], + "index": 5.25 + }, + { + "type": "image", + "bbox": [ + 130, + 384, + 475, + 472 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 130, + 384, + 475, + 472 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 130, + 384, + 475, + 472 + ], + "spans": [ + { + "bbox": [ + 130, + 384, + 475, + 472 + ], + "score": 0.971, + "type": "image", + "image_path": "aefe5703a6af1bb98f484da513d1f7861b5ff52440d53d4cfceab98875c791d8.jpg" + } + ] + } + ], + "index": 18, + "virtual_lines": [ + { + "bbox": [ + 130, + 384, + 475, + 413.3333333333333 + ], + "spans": [], + "index": 17 + }, + { + "bbox": [ + 130, + 413.3333333333333, + 475, + 442.66666666666663 + ], + "spans": [], + "index": 18 + }, + { + "bbox": [ + 130, + 442.66666666666663, + 475, + 471.99999999999994 + ], + "spans": [], + "index": 19 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 105, + 477, + 504, + 508 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 477, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 505, + 488 + ], + "score": 1.0, + "content": "Figure 3: Robotics environments and the results under deployment constraints (10 deployments with batch sizes", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 487, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 487, + 505, + 498 + ], + "score": 1.0, + "content": "of 25k). The performances are averaged over 5 seeds. BREMEN seems the only method that shows both stable", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 497, + 419, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 419, + 509 + ], + "score": 1.0, + "content": "improvement and solving tasks without large degradation or sub-optimal convergence.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 107, + 530, + 505, + 586 + ], + "lines": [ + { + "bbox": [ + 105, + 530, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 530, + 314, + 543 + ], + "score": 1.0, + "content": "we limit the batch size at each deployment as only", + "type": "text" + }, + { + "bbox": [ + 314, + 531, + 331, + 541 + ], + "score": 0.68, + "content": "2 5 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 331, + 530, + 505, + 543 + ], + "score": 1.0, + "content": ". Figure 3 presents the reaching tasks with", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 540, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 505, + 554 + ], + "score": 1.0, + "content": "Fetch robot and 20-DoF shadow hand (Plappert et al., 2018), and the experimental results in both", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 552, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 505, + 565 + ], + "score": 1.0, + "content": "environments. Only BREMEN shows stable improvement and high performance, while other offline", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 563, + 506, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 506, + 576 + ], + "score": 1.0, + "content": "and online algorithms fail to learn. These results suggest that a model-based method is a desirable", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 574, + 495, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 495, + 587 + ], + "score": 1.0, + "content": "approach for satisfying practical requirements in robotics, i.e. sample and deployment efficiency.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25 + }, + { + "type": "title", + "bbox": [ + 108, + 600, + 426, + 612 + ], + "lines": [ + { + "bbox": [ + 105, + 600, + 428, + 614 + ], + "spans": [ + { + "bbox": [ + 105, + 600, + 428, + 614 + ], + "score": 1.0, + "content": "5.3 ABLATION: EVALUATING EFFECTIVENESS OF IMPLICIT KL CONTROL", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 622, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 621, + 506, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 506, + 634 + ], + "score": 1.0, + "content": "In this section, we present an experiment to better understand the effect of BREMEN’s implicit", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 633, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 646 + ], + "score": 1.0, + "content": "regularization. Figure 4 shows the KL divergence of learned policies from the last deployed policy.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 643, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 506, + 656 + ], + "score": 1.0, + "content": "We compare BREMEN to variants of BREMEN that use an explicit KL penalty on value instead of BC", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "score": 1.0, + "content": "initialization (conservative KL trust-region updates are still used). We find that the explicit KL without", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "behavior initialization variants learn policies that move farther away from the last deployed policy", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "than behavior initialized policies. This suggests that the implicit behavior regularization employed by", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "BREMEN is more effective as a conservative policy learning protocol. In addition, to assess the effect", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "score": 1.0, + "content": "of repeated behavior cloning initialization, we also evaluate a variant of BREMEN without behavior", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "cloning re-initialization (grey). This variant works in easier environments (Ant, Halfcheetah), but", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "does not show remarkable progress in more challenging ones with termination (Hopper, Walker2d).", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 33.5 + } + ], + "page_idx": 6, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 292, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "score": 1.0, + "content": "7", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 120, + 81, + 493, + 209 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 120, + 81, + 493, + 209 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 120, + 81, + 493, + 209 + ], + "spans": [ + { + "bbox": [ + 120, + 81, + 493, + 209 + ], + "score": 0.968, + "type": "image", + "image_path": "6a1cb8fc593fa991de860c81499864a36dc243a21b814426030744b691e27217.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 120, + 81, + 493, + 123.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 120, + 123.66666666666666, + 493, + 166.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 120, + 166.33333333333331, + 493, + 208.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 213, + 506, + 353 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 213, + 506, + 225 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 506, + 225 + ], + "score": 1.0, + "content": "Figure 2: Evaluation of BREMEN with the existing methods (ME-TRPO, SAC, BCQ, BRAC) under deployment", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 223, + 506, + 235 + ], + "spans": [ + { + "bbox": [ + 104, + 223, + 506, + 235 + ], + "score": 1.0, + "content": "constraints (to 5-10 deployments with batch sizes of 200k and 100k). The average cumulative rewards and their", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 234, + 506, + 245 + ], + "spans": [ + { + "bbox": [ + 106, + 234, + 506, + 245 + ], + "score": 1.0, + "content": "standard deviations with 5 random seeds are shown. Vertical dotted lines represent where each policy deployment", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 243, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 506, + 255 + ], + "score": 1.0, + "content": "and data collection happen. BREMEN is able to learn successful policies with only 5-10 deployments, while the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 254, + 506, + 265 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 506, + 265 + ], + "score": 1.0, + "content": "state-of-the-art off-policy (SAC), model-based (ME-TRPO), and recursively-applied offline RL algorithms (BCQ,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 263, + 506, + 276 + ], + "spans": [ + { + "bbox": [ + 105, + 263, + 506, + 276 + ], + "score": 1.0, + "content": "BRAC) often struggle to make any progress. For completeness, we show ME-TRPO(online) and SAC(online)", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 273, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 506, + 285 + ], + "score": 1.0, + "content": "which are their original optimal learning curves without deployment constraints, plotted with respect to samples", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "score": 1.0, + "content": "normalized by the batch size. While SAC(online) substantially outperforms BREMEN in sample efficiency, it", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 293, + 506, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 506, + 305 + ], + "score": 1.0, + "content": "uses 1 deployment per sample, leading to 100k-500k deployments required for learning. Interestingly, BREMEN", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 302, + 506, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 506, + 315 + ], + "score": 1.0, + "content": "achieves even better performance than the original ME-TRPO(online), suggesting the effectiveness of implicit", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 312, + 505, + 325 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 505, + 325 + ], + "score": 1.0, + "content": "behavior regularization. For SAC and ME-TRPO under deployment-constrained evaluation, their batch size", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 323, + 505, + 334 + ], + "spans": [ + { + "bbox": [ + 106, + 323, + 505, + 334 + ], + "score": 1.0, + "content": "between policy deployments differs substantially from their standard settings, and therefore we performed", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 333, + 506, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 506, + 346 + ], + "score": 1.0, + "content": "extensive hyper-parameter search on the relevant parameters such as the number of policy updates between", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 343, + 272, + 354 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 272, + 354 + ], + "score": 1.0, + "content": "deployments, as discussed in Appendix F.2.1.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 9.5 + } + ], + "index": 5.25 + }, + { + "type": "image", + "bbox": [ + 130, + 384, + 475, + 472 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 130, + 384, + 475, + 472 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 130, + 384, + 475, + 472 + ], + "spans": [ + { + "bbox": [ + 130, + 384, + 475, + 472 + ], + "score": 0.971, + "type": "image", + "image_path": "aefe5703a6af1bb98f484da513d1f7861b5ff52440d53d4cfceab98875c791d8.jpg" + } + ] + } + ], + "index": 18, + "virtual_lines": [ + { + "bbox": [ + 130, + 384, + 475, + 413.3333333333333 + ], + "spans": [], + "index": 17 + }, + { + "bbox": [ + 130, + 413.3333333333333, + 475, + 442.66666666666663 + ], + "spans": [], + "index": 18 + }, + { + "bbox": [ + 130, + 442.66666666666663, + 475, + 471.99999999999994 + ], + "spans": [], + "index": 19 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 105, + 477, + 504, + 508 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 477, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 505, + 488 + ], + "score": 1.0, + "content": "Figure 3: Robotics environments and the results under deployment constraints (10 deployments with batch sizes", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 487, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 487, + 505, + 498 + ], + "score": 1.0, + "content": "of 25k). The performances are averaged over 5 seeds. BREMEN seems the only method that shows both stable", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 497, + 419, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 419, + 509 + ], + "score": 1.0, + "content": "improvement and solving tasks without large degradation or sub-optimal convergence.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 107, + 530, + 505, + 586 + ], + "lines": [], + "index": 25, + "bbox_fs": [ + 105, + 530, + 506, + 587 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 108, + 600, + 426, + 612 + ], + "lines": [ + { + "bbox": [ + 105, + 600, + 428, + 614 + ], + "spans": [ + { + "bbox": [ + 105, + 600, + 428, + 614 + ], + "score": 1.0, + "content": "5.3 ABLATION: EVALUATING EFFECTIVENESS OF IMPLICIT KL CONTROL", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 622, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 621, + 506, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 506, + 634 + ], + "score": 1.0, + "content": "In this section, we present an experiment to better understand the effect of BREMEN’s implicit", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 633, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 646 + ], + "score": 1.0, + "content": "regularization. Figure 4 shows the KL divergence of learned policies from the last deployed policy.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 643, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 506, + 656 + ], + "score": 1.0, + "content": "We compare BREMEN to variants of BREMEN that use an explicit KL penalty on value instead of BC", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "score": 1.0, + "content": "initialization (conservative KL trust-region updates are still used). We find that the explicit KL without", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "behavior initialization variants learn policies that move farther away from the last deployed policy", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "than behavior initialized policies. This suggests that the implicit behavior regularization employed by", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "BREMEN is more effective as a conservative policy learning protocol. In addition, to assess the effect", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "score": 1.0, + "content": "of repeated behavior cloning initialization, we also evaluate a variant of BREMEN without behavior", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "cloning re-initialization (grey). This variant works in easier environments (Ant, Halfcheetah), but", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "does not show remarkable progress in more challenging ones with termination (Hopper, Walker2d).", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 621, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 117, + 80, + 496, + 224 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 117, + 80, + 496, + 224 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 117, + 80, + 496, + 224 + ], + "spans": [ + { + "bbox": [ + 117, + 80, + 496, + 224 + ], + "score": 0.973, + "type": "image", + "image_path": "caaaeaae5c063a15f89b51e7364e62582bf4f0db0e551d24fb5de280da818a2c.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 117, + 80, + 496, + 128.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 117, + 128.0, + 496, + 176.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 117, + 176.0, + 496, + 224.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 228, + 505, + 268 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 227, + 506, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 227, + 506, + 240 + ], + "score": 1.0, + "content": "Figure 4: We examine average cumulative rewards (top) and corresponding KL divergence between the last", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 237, + 506, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 506, + 249 + ], + "score": 1.0, + "content": "deployed policy and the target policy (bottom) with batch size 200K in limited deployment settings. The behavior", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 246, + 504, + 259 + ], + "spans": [ + { + "bbox": [ + 106, + 246, + 504, + 259 + ], + "score": 1.0, + "content": "initialized policy remains close to the last deployed policy during improvement without explicit value penalty", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 257, + 363, + 270 + ], + "spans": [ + { + "bbox": [ + 107, + 257, + 170, + 269 + ], + "score": 0.91, + "content": "- \\alpha D _ { \\mathrm { K L } } ( { \\bar { \\pi _ { \\theta } } } \\| { \\hat { \\pi } } _ { \\beta } )", + "type": "inline_equation" + }, + { + "bbox": [ + 171, + 257, + 352, + 270 + ], + "score": 1.0, + "content": ". The explicit penalty is controlled by a coefficient", + "type": "text" + }, + { + "bbox": [ + 352, + 259, + 359, + 267 + ], + "score": 0.61, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 257, + 363, + 270 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 107, + 289, + 504, + 312 + ], + "lines": [ + { + "bbox": [ + 105, + 288, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 505, + 302 + ], + "score": 1.0, + "content": "This result empirically supports the need for repeated behavior initialization after each deployment.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 300, + 351, + 313 + ], + "spans": [ + { + "bbox": [ + 106, + 300, + 351, + 313 + ], + "score": 1.0, + "content": "The results of further experiments are shown in Appendix G.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5 + }, + { + "type": "title", + "bbox": [ + 108, + 328, + 211, + 340 + ], + "lines": [ + { + "bbox": [ + 105, + 327, + 213, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 213, + 343 + ], + "score": 1.0, + "content": "6 RELATED WORK", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 353, + 505, + 639 + ], + "lines": [ + { + "bbox": [ + 106, + 353, + 505, + 364 + ], + "spans": [ + { + "bbox": [ + 106, + 353, + 505, + 364 + ], + "score": 1.0, + "content": "Deployment Efficiency and Offline RL Although we are not aware of any previous works which", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 364, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 364, + 506, + 376 + ], + "score": 1.0, + "content": "explicitly proposed the concept of deployment efficiency, its necessity in many real-world applications", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 374, + 506, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 506, + 387 + ], + "score": 1.0, + "content": "has been generally known. One may consider previously proposed semi-batch RL algorithms (Ernst", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 384, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 104, + 384, + 506, + 399 + ], + "score": 1.0, + "content": "et al., 2005; Lange et al., 2012; Singh et al., 1994; Roux, 2016) or theoretical analysis of switching", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 396, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 505, + 408 + ], + "score": 1.0, + "content": "cost under the tabular PAC-MDP settings (Bai et al., 2019; Guo & Brunskill, 2015) as approaching this", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "score": 1.0, + "content": "issue. More recently, a related but distinct problem known as offline RL has gained popularity (Levine", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "score": 1.0, + "content": "et al., 2020; Wu et al., 2019; Agarwal et al., 2019; Kumar et al., 2020). These works consider an", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 428, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 104, + 428, + 505, + 443 + ], + "score": 1.0, + "content": "extreme version of 1 deployment, and typically collect the static batch with a partially trained policy", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 441, + 506, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 506, + 453 + ], + "score": 1.0, + "content": "rather than a random policy. While offline RL has shown promising results for a variety of real-world", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 451, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 506, + 465 + ], + "score": 1.0, + "content": "applications, such as robotics (Mandlekar et al., 2019), dialogue systems (Jaques et al., 2019), or", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "medical treatments (Gottesman et al., 2018), these algorithms struggle when learning a policy from", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 474, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 505, + 485 + ], + "score": 1.0, + "content": "scratch or when the dataset is small. Nevertheless, common themes of many offline RL algorithms", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 484, + 506, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 506, + 496 + ], + "score": 1.0, + "content": "– regularizing the learned policy to the behavior policy (Fujimoto et al., 2019; Kumar et al., 2019;", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 495, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 506, + 507 + ], + "score": 1.0, + "content": "Siegel et al., 2020; Wu et al., 2019) and utilizing ensembles to handle uncertainty (Kumar et al.,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "score": 1.0, + "content": "2019; Wu et al., 2019) – served as inspirations for the proposed our algorithm. A major difference", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 516, + 506, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 506, + 529 + ], + "score": 1.0, + "content": "of BREMEN from prior works is that the target policy is not explicitly forced to stick close to", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 527, + 506, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 506, + 541 + ], + "score": 1.0, + "content": "the estimated behavior policy through the policy update except for the initial iteration. Rather,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 538, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 506, + 551 + ], + "score": 1.0, + "content": "BREMEN employs a more implicit regularization by initializing the learned policy with a behavior", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 549, + 506, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 506, + 563 + ], + "score": 1.0, + "content": "cloned policy and then applying conservative trust-region updates. Another major difference is", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "score": 1.0, + "content": "the application of model-based approaches to fully offline settings, which has not been extensively", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 572, + 506, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 506, + 584 + ], + "score": 1.0, + "content": "studied in prior works (Levine et al., 2020), except the two concurrent works (Kidambi et al., 2020;", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 582, + 505, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 505, + 596 + ], + "score": 1.0, + "content": "Yu et al., 2020) that study pessimistic or uncertainty penalized MDPs with guarantees – closely", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "related to Liu et al. (2019). By contrast, our work shows that a simple technique can already enable", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 604, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 506, + 617 + ], + "score": 1.0, + "content": "model-based offline algorithms to significantly outperform the prior model-free methods, and is, to", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "the best of our knowledge, the first to define and extensively evaluate deployment efficiency with", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 627, + 198, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 627, + 198, + 639 + ], + "score": 1.0, + "content": "recursive experiments.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "score": 1.0, + "content": "Model-Based RL There are many types of model-based RL algorithms (Sutton, 1991; Deisenroth", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "score": 1.0, + "content": "& Rasmussen, 2011; Heess et al., 2015). A simple algorithmic choice is Dyna-style (Sutton, 1991),", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 666, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 677 + ], + "score": 1.0, + "content": "which uses a parameterized model to estimate the true MDP transition function, stochastically", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 677, + 505, + 688 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 688 + ], + "score": 1.0, + "content": "mapping states and actions to next states. The dynamics model can then serve as a simulator of the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 688, + 506, + 699 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 699 + ], + "score": 1.0, + "content": "environment during policy updates. Dyna-style algorithms often suffer from the distributional shift,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 699, + 505, + 710 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 710 + ], + "score": 1.0, + "content": "also known as model bias, which leads RL agents to exploit regions where the data is insufficient, and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 710, + 506, + 721 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 506, + 721 + ], + "score": 1.0, + "content": "significant performance degradation. A variety of remedies have been proposed to relieve the issue of", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 720, + 505, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 732 + ], + "score": 1.0, + "content": "model bias, such as the use of multiple dynamics models as an ensemble (Chua et al., 2018; Kurutach", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 39.5 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 292, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "score": 1.0, + "content": "8", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 117, + 80, + 496, + 224 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 117, + 80, + 496, + 224 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 117, + 80, + 496, + 224 + ], + "spans": [ + { + "bbox": [ + 117, + 80, + 496, + 224 + ], + "score": 0.973, + "type": "image", + "image_path": "caaaeaae5c063a15f89b51e7364e62582bf4f0db0e551d24fb5de280da818a2c.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 117, + 80, + 496, + 128.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 117, + 128.0, + 496, + 176.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 117, + 176.0, + 496, + 224.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 228, + 505, + 268 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 227, + 506, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 227, + 506, + 240 + ], + "score": 1.0, + "content": "Figure 4: We examine average cumulative rewards (top) and corresponding KL divergence between the last", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 237, + 506, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 506, + 249 + ], + "score": 1.0, + "content": "deployed policy and the target policy (bottom) with batch size 200K in limited deployment settings. The behavior", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 246, + 504, + 259 + ], + "spans": [ + { + "bbox": [ + 106, + 246, + 504, + 259 + ], + "score": 1.0, + "content": "initialized policy remains close to the last deployed policy during improvement without explicit value penalty", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 257, + 363, + 270 + ], + "spans": [ + { + "bbox": [ + 107, + 257, + 170, + 269 + ], + "score": 0.91, + "content": "- \\alpha D _ { \\mathrm { K L } } ( { \\bar { \\pi _ { \\theta } } } \\| { \\hat { \\pi } } _ { \\beta } )", + "type": "inline_equation" + }, + { + "bbox": [ + 171, + 257, + 352, + 270 + ], + "score": 1.0, + "content": ". The explicit penalty is controlled by a coefficient", + "type": "text" + }, + { + "bbox": [ + 352, + 259, + 359, + 267 + ], + "score": 0.61, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 257, + 363, + 270 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "list", + "bbox": [ + 107, + 289, + 504, + 312 + ], + "lines": [ + { + "bbox": [ + 105, + 288, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 505, + 302 + ], + "score": 1.0, + "content": "This result empirically supports the need for repeated behavior initialization after each deployment.", + "type": "text" + } + ], + "index": 7, + "is_list_end_line": true + }, + { + "bbox": [ + 106, + 300, + 351, + 313 + ], + "spans": [ + { + "bbox": [ + 106, + 300, + 351, + 313 + ], + "score": 1.0, + "content": "The results of further experiments are shown in Appendix G.", + "type": "text" + } + ], + "index": 8, + "is_list_start_line": true, + "is_list_end_line": true + } + ], + "index": 7.5, + "bbox_fs": [ + 105, + 288, + 505, + 313 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 328, + 211, + 340 + ], + "lines": [ + { + "bbox": [ + 105, + 327, + 213, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 213, + 343 + ], + "score": 1.0, + "content": "6 RELATED WORK", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 353, + 505, + 639 + ], + "lines": [ + { + "bbox": [ + 106, + 353, + 505, + 364 + ], + "spans": [ + { + "bbox": [ + 106, + 353, + 505, + 364 + ], + "score": 1.0, + "content": "Deployment Efficiency and Offline RL Although we are not aware of any previous works which", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 364, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 364, + 506, + 376 + ], + "score": 1.0, + "content": "explicitly proposed the concept of deployment efficiency, its necessity in many real-world applications", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 374, + 506, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 506, + 387 + ], + "score": 1.0, + "content": "has been generally known. One may consider previously proposed semi-batch RL algorithms (Ernst", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 384, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 104, + 384, + 506, + 399 + ], + "score": 1.0, + "content": "et al., 2005; Lange et al., 2012; Singh et al., 1994; Roux, 2016) or theoretical analysis of switching", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 396, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 505, + 408 + ], + "score": 1.0, + "content": "cost under the tabular PAC-MDP settings (Bai et al., 2019; Guo & Brunskill, 2015) as approaching this", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "score": 1.0, + "content": "issue. More recently, a related but distinct problem known as offline RL has gained popularity (Levine", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "score": 1.0, + "content": "et al., 2020; Wu et al., 2019; Agarwal et al., 2019; Kumar et al., 2020). These works consider an", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 428, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 104, + 428, + 505, + 443 + ], + "score": 1.0, + "content": "extreme version of 1 deployment, and typically collect the static batch with a partially trained policy", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 441, + 506, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 506, + 453 + ], + "score": 1.0, + "content": "rather than a random policy. While offline RL has shown promising results for a variety of real-world", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 451, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 506, + 465 + ], + "score": 1.0, + "content": "applications, such as robotics (Mandlekar et al., 2019), dialogue systems (Jaques et al., 2019), or", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "medical treatments (Gottesman et al., 2018), these algorithms struggle when learning a policy from", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 474, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 505, + 485 + ], + "score": 1.0, + "content": "scratch or when the dataset is small. Nevertheless, common themes of many offline RL algorithms", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 484, + 506, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 506, + 496 + ], + "score": 1.0, + "content": "– regularizing the learned policy to the behavior policy (Fujimoto et al., 2019; Kumar et al., 2019;", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 495, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 506, + 507 + ], + "score": 1.0, + "content": "Siegel et al., 2020; Wu et al., 2019) and utilizing ensembles to handle uncertainty (Kumar et al.,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "score": 1.0, + "content": "2019; Wu et al., 2019) – served as inspirations for the proposed our algorithm. A major difference", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 516, + 506, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 506, + 529 + ], + "score": 1.0, + "content": "of BREMEN from prior works is that the target policy is not explicitly forced to stick close to", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 527, + 506, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 506, + 541 + ], + "score": 1.0, + "content": "the estimated behavior policy through the policy update except for the initial iteration. Rather,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 538, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 506, + 551 + ], + "score": 1.0, + "content": "BREMEN employs a more implicit regularization by initializing the learned policy with a behavior", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 549, + 506, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 506, + 563 + ], + "score": 1.0, + "content": "cloned policy and then applying conservative trust-region updates. Another major difference is", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "score": 1.0, + "content": "the application of model-based approaches to fully offline settings, which has not been extensively", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 572, + 506, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 506, + 584 + ], + "score": 1.0, + "content": "studied in prior works (Levine et al., 2020), except the two concurrent works (Kidambi et al., 2020;", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 582, + 505, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 505, + 596 + ], + "score": 1.0, + "content": "Yu et al., 2020) that study pessimistic or uncertainty penalized MDPs with guarantees – closely", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "related to Liu et al. (2019). By contrast, our work shows that a simple technique can already enable", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 604, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 506, + 617 + ], + "score": 1.0, + "content": "model-based offline algorithms to significantly outperform the prior model-free methods, and is, to", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "the best of our knowledge, the first to define and extensively evaluate deployment efficiency with", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 627, + 198, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 627, + 198, + 639 + ], + "score": 1.0, + "content": "recursive experiments.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 22.5, + "bbox_fs": [ + 104, + 353, + 506, + 639 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "score": 1.0, + "content": "Model-Based RL There are many types of model-based RL algorithms (Sutton, 1991; Deisenroth", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "score": 1.0, + "content": "& Rasmussen, 2011; Heess et al., 2015). A simple algorithmic choice is Dyna-style (Sutton, 1991),", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 666, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 677 + ], + "score": 1.0, + "content": "which uses a parameterized model to estimate the true MDP transition function, stochastically", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 677, + 505, + 688 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 688 + ], + "score": 1.0, + "content": "mapping states and actions to next states. The dynamics model can then serve as a simulator of the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 688, + 506, + 699 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 699 + ], + "score": 1.0, + "content": "environment during policy updates. Dyna-style algorithms often suffer from the distributional shift,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 699, + 505, + 710 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 710 + ], + "score": 1.0, + "content": "also known as model bias, which leads RL agents to exploit regions where the data is insufficient, and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 710, + 506, + 721 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 506, + 721 + ], + "score": 1.0, + "content": "significant performance degradation. A variety of remedies have been proposed to relieve the issue of", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 720, + 505, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 732 + ], + "score": 1.0, + "content": "model bias, such as the use of multiple dynamics models as an ensemble (Chua et al., 2018; Kurutach", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 81, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 505, + 95 + ], + "score": 1.0, + "content": "et al., 2018; Janner et al., 2019), meta-learning (Clavera et al., 2018), energy-based regularizer (Boney", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "score": 1.0, + "content": "et al., 2019), game-theoretic framework (Rajeswaran et al., 2020), and explicit penalty for unknown", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 506, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 506, + 117 + ], + "score": 1.0, + "content": "states (Kidambi et al., 2020; Yu et al., 2020). Notably, we have employed a subset of these remedies –", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "model ensembles and trust-region updates (Kurutach et al., 2018) – for BREMEN. Compared to prior", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 126, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 106, + 126, + 506, + 139 + ], + "score": 1.0, + "content": "works, our work is notable for using BC initialization in conjunction with trust-region updates to", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 137, + 506, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 506, + 149 + ], + "score": 1.0, + "content": "alleviate the distribution shift of the learned policy from the dataset used to train the dynamics model.", + "type": "text", + "cross_page": true + } + ], + "index": 5 + } + ], + "index": 39.5, + "bbox_fs": [ + 105, + 642, + 506, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 149 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 505, + 95 + ], + "score": 1.0, + "content": "et al., 2018; Janner et al., 2019), meta-learning (Clavera et al., 2018), energy-based regularizer (Boney", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "score": 1.0, + "content": "et al., 2019), game-theoretic framework (Rajeswaran et al., 2020), and explicit penalty for unknown", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 506, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 506, + 117 + ], + "score": 1.0, + "content": "states (Kidambi et al., 2020; Yu et al., 2020). Notably, we have employed a subset of these remedies –", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "model ensembles and trust-region updates (Kurutach et al., 2018) – for BREMEN. 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MOPO: Model-based offline policy optimization. arXiv preprint arXiv:2005.13239,", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 115, + 718, + 143, + 733 + ], + "spans": [ + { + "bbox": [ + 115, + 718, + 143, + 733 + ], + "score": 1.0, + "content": "2020.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 46, + "bbox_fs": [ + 105, + 697, + 507, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 161, + 94 + ], + "lines": [ + { + "bbox": [ + 106, + 81, + 163, + 96 + ], + "spans": [ + { + "bbox": [ + 106, + 81, + 163, + 96 + ], + "score": 1.0, + "content": "APPENDIX", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "title", + "bbox": [ + 107, + 106, + 453, + 121 + ], + "lines": [ + { + "bbox": [ + 105, + 106, + 455, + 122 + ], + "spans": [ + { + "bbox": [ + 105, + 106, + 455, + 122 + ], + "score": 1.0, + "content": "A IMPLICIT KL CONTROL FROM A MATHEMATICAL PERSPECTIVE", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 106, + 131, + 505, + 212 + ], + "lines": [ + { + "bbox": [ + 106, + 132, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 106, + 132, + 505, + 144 + ], + "score": 1.0, + "content": "We can intuitively understand that behavior cloning initialization with trust-region updates works as", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 143, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 505, + 156 + ], + "score": 1.0, + "content": "a regularization of distributional shift, and this can be supported by theory. Following the notation", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 154, + 504, + 166 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 504, + 166 + ], + "score": 1.0, + "content": "of Janner et al. (2019), we denote the generalization error of a dynamics model on the state distribution", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 164, + 506, + 180 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 243, + 180 + ], + "score": 1.0, + "content": "under the true behavior policy as", + "type": "text" + }, + { + "bbox": [ + 244, + 165, + 473, + 179 + ], + "score": 0.91, + "content": "\\begin{array} { r } { \\epsilon _ { m } = \\operatorname* { m a x } _ { t } \\mathbb { E } _ { s \\sim d _ { t } ^ { \\pi _ { b } } } D _ { T V } ( \\bar { p ( } s _ { t + 1 } | s _ { t } , a _ { t } ) | | p _ { \\phi } ( s _ { t + 1 } | s _ { t } , a _ { t } ) ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 474, + 164, + 506, + 180 + ], + "score": 1.0, + "content": ", where", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 177, + 505, + 190 + ], + "spans": [ + { + "bbox": [ + 107, + 178, + 128, + 189 + ], + "score": 0.89, + "content": "D _ { T V }", + "type": "inline_equation" + }, + { + "bbox": [ + 129, + 177, + 372, + 190 + ], + "score": 1.0, + "content": "represents the total variation distance between true dynamics", + "type": "text" + }, + { + "bbox": [ + 372, + 181, + 379, + 189 + ], + "score": 0.76, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 177, + 455, + 190 + ], + "score": 1.0, + "content": "and learned model", + "type": "text" + }, + { + "bbox": [ + 455, + 180, + 467, + 190 + ], + "score": 0.83, + "content": "p _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 467, + 177, + 505, + 190 + ], + "score": 1.0, + "content": ". We also", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 189, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 106, + 189, + 314, + 201 + ], + "score": 1.0, + "content": "denote the distribution shift on the target policy as", + "type": "text" + }, + { + "bbox": [ + 314, + 189, + 413, + 201 + ], + "score": 0.84, + "content": "\\begin{array} { r } { \\operatorname* { m a x } _ { s } D _ { T V } ( \\pi _ { b } | | \\pi ) \\le \\epsilon _ { \\pi } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 414, + 189, + 505, + 201 + ], + "score": 1.0, + "content": ". A bound relating the", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 199, + 499, + 213 + ], + "spans": [ + { + "bbox": [ + 105, + 199, + 154, + 213 + ], + "score": 1.0, + "content": "true returns", + "type": "text" + }, + { + "bbox": [ + 155, + 200, + 173, + 212 + ], + "score": 0.91, + "content": "\\eta [ \\pi ]", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 199, + 263, + 213 + ], + "score": 1.0, + "content": "and the model returns", + "type": "text" + }, + { + "bbox": [ + 263, + 200, + 281, + 212 + ], + "score": 0.95, + "content": "\\hat { \\eta } [ \\pi ]", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 199, + 499, + 213 + ], + "score": 1.0, + "content": "on the target policy is given in Janner et al. (2019) as,", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5 + }, + { + "type": "interline_equation", + "bbox": [ + 202, + 215, + 408, + 243 + ], + "lines": [ + { + "bbox": [ + 202, + 215, + 408, + 243 + ], + "spans": [ + { + "bbox": [ + 202, + 215, + 408, + 243 + ], + "score": 0.92, + "content": "\\eta [ \\pi ] \\ge \\hat { \\eta } [ \\pi ] - \\left[ \\frac { 2 \\gamma r _ { m a x } ( \\epsilon _ { m } + 2 \\epsilon _ { \\pi } ) } { ( 1 - \\gamma ) ^ { 2 } } + \\frac { 4 r _ { m a x } \\epsilon _ { \\pi } } { ( 1 - \\gamma ) } \\right] .", + "type": "interline_equation", + "image_path": "d61ef7ba6dbba742a282990d7b12e361b9ee354446876eed6f9a57f566e8039b.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 202, + 215, + 408, + 243 + ], + "spans": [], + "index": 9 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 245, + 505, + 279 + ], + "lines": [ + { + "bbox": [ + 105, + 244, + 506, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 506, + 258 + ], + "score": 1.0, + "content": "This bound guarantees the improvement under the true returns as long as the improvement under", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 256, + 506, + 268 + ], + "spans": [ + { + "bbox": [ + 105, + 256, + 395, + 268 + ], + "score": 1.0, + "content": "the model returns increases by more than the slack in the bound due to", + "type": "text" + }, + { + "bbox": [ + 395, + 258, + 421, + 268 + ], + "score": 0.9, + "content": "\\epsilon _ { m } , \\epsilon _ { \\pi }", + "type": "inline_equation" + }, + { + "bbox": [ + 422, + 256, + 506, + 268 + ], + "score": 1.0, + "content": "(Janner et al., 2019;", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 266, + 189, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 189, + 279 + ], + "score": 1.0, + "content": "Levine et al., 2020).", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 106, + 283, + 505, + 339 + ], + "lines": [ + { + "bbox": [ + 106, + 283, + 505, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 283, + 505, + 297 + ], + "score": 1.0, + "content": "We may relate this bound to the specific learning employed by BREMEN, which includes dynamics", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 294, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 505, + 309 + ], + "score": 1.0, + "content": "model learning, behavior cloning policy initialization, and conservative KL-based trust-region policy", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 305, + 505, + 318 + ], + "spans": [ + { + "bbox": [ + 106, + 305, + 505, + 318 + ], + "score": 1.0, + "content": "updates. 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Suppose we apply the idealized BREMEN on a", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 352, + 474, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 138, + 367 + ], + "score": 1.0, + "content": "dataset", + "type": "text" + }, + { + "bbox": [ + 138, + 354, + 146, + 363 + ], + "score": 0.77, + "content": "\\mathcal { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 352, + 194, + 367 + ], + "score": 1.0, + "content": ", and define", + "type": "text" + }, + { + "bbox": [ + 195, + 354, + 218, + 366 + ], + "score": 0.88, + "content": "\\epsilon _ { \\beta } , \\epsilon _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 352, + 474, + 367 + ], + "score": 1.0, + "content": "in terms of the behavior cloning and dynamics model losses as,", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18.5 + }, + { + "type": "interline_equation", + "bbox": [ + 179, + 369, + 432, + 416 + ], + "lines": [ + { + "bbox": [ + 179, + 369, + 432, + 416 + ], + "spans": [ + { + "bbox": [ + 179, + 369, + 432, + 416 + ], + "score": 0.95, + "content": "\\begin{array} { r l } & { \\epsilon _ { \\beta } : = \\underset { s } { \\operatorname* { s u p } } \\mathbb { E } _ { a \\sim \\mathcal { D } ( - | s ) } [ \\| a - \\hat { \\pi } _ { \\beta } \\left( s \\right) \\| _ { 2 } ^ { 2 } / 2 ] - \\mathcal { H } ( \\pi _ { b } ( - | s ) ) } \\\\ & { \\epsilon _ { \\phi } : = \\underset { s , a } { \\operatorname* { s u p } } \\mathbb { E } _ { s ^ { \\prime } \\sim \\mathcal { D } ( - | s , a ) } \\left[ \\| s ^ { \\prime } - \\hat { f } _ { \\phi } ( s , a ) \\| _ { 2 } ^ { 2 } / 2 \\right] - \\mathcal { H } ( p ( - | s , a ) ) , } \\end{array}", + "type": "interline_equation", + "image_path": "c2f2c3d72e588942d1f90e27679108d3e13e651aa575885e47b8e07354fb2315.jpg" + } + ] + } + ], + "index": 21, + "virtual_lines": [ + { + "bbox": [ + 179, + 369, + 432, + 384.6666666666667 + ], + "spans": [], + "index": 20 + }, + { + "bbox": [ + 179, + 384.6666666666667, + 432, + 400.33333333333337 + ], + "spans": [], + "index": 21 + }, + { + "bbox": [ + 179, + 400.33333333333337, + 432, + 416.00000000000006 + ], + "spans": [], + "index": 22 + } + ] + }, + { + "type": "text", + "bbox": [ + 104, + 419, + 505, + 444 + ], + "lines": [ + { + "bbox": [ + 106, + 418, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 106, + 418, + 132, + 432 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 420, + 142, + 429 + ], + "score": 0.78, + "content": "\\mathcal { H }", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 418, + 338, + 432 + ], + "score": 1.0, + "content": "denotes the Shannon entropy. If one then applies", + "type": "text" + }, + { + "bbox": [ + 338, + 420, + 347, + 429 + ], + "score": 0.67, + "content": "T", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 418, + 505, + 432 + ], + "score": 1.0, + "content": "KL-based trust-region steps of step size", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 107, + 430, + 485, + 444 + ], + "spans": [ + { + "bbox": [ + 107, + 433, + 112, + 442 + ], + "score": 0.71, + "content": "\\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 113, + 431, + 348, + 444 + ], + "score": 1.0, + "content": "(Equation 4) using stochastic dynamics models with mean", + "type": "text" + }, + { + "bbox": [ + 348, + 430, + 359, + 444 + ], + "score": 0.9, + "content": "\\hat { f } _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 431, + 455, + 444 + ], + "score": 1.0, + "content": "and standard deviation", + "type": "text" + }, + { + "bbox": [ + 455, + 433, + 461, + 442 + ], + "score": 0.52, + "content": "^ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 461, + 431, + 485, + 444 + ], + "score": 1.0, + "content": ", then", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5 + }, + { + "type": "interline_equation", + "bbox": [ + 172, + 447, + 438, + 476 + ], + "lines": [ + { + "bbox": [ + 172, + 447, + 438, + 476 + ], + "spans": [ + { + "bbox": [ + 172, + 447, + 438, + 476 + ], + "score": 0.94, + "content": "\\epsilon _ { \\pi } = \\sqrt { \\frac { 1 } { 2 } \\epsilon _ { \\beta } + \\frac { d _ { a } } { 4 } \\log 2 \\pi } + T \\sqrt { \\frac { 1 } { 2 } \\delta } ; \\epsilon _ { m } \\leq \\sqrt { \\frac { 1 } { 2 } \\epsilon _ { \\phi } + \\frac { d _ { s } } { 4 } \\log 2 \\pi } ,", + "type": "interline_equation", + "image_path": "8ccdfa3eb115b464fecd2fe3267fdfdd209a81219d9b0a18cf587294a3b2cc52.jpg" + } + ] + } + ], + "index": 26, + "virtual_lines": [ + { + "bbox": [ + 172, + 447, + 438, + 456.6666666666667 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 172, + 456.6666666666667, + 438, + 466.33333333333337 + ], + "spans": [], + "index": 26 + }, + { + "bbox": [ + 172, + 466.33333333333337, + 438, + 476.00000000000006 + ], + "spans": [], + "index": 27 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 479, + 369, + 491 + ], + "lines": [ + { + "bbox": [ + 105, + 477, + 370, + 493 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 133, + 493 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 480, + 144, + 490 + ], + "score": 0.86, + "content": "d _ { a }", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 477, + 163, + 493 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 163, + 479, + 173, + 490 + ], + "score": 0.86, + "content": "d _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 477, + 370, + 493 + ], + "score": 1.0, + "content": "denotes the dimension of action and state space.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 108, + 502, + 446, + 514 + ], + "lines": [ + { + "bbox": [ + 105, + 500, + 448, + 517 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 206, + 517 + ], + "score": 1.0, + "content": "Proof. We first consider", + "type": "text" + }, + { + "bbox": [ + 206, + 504, + 216, + 514 + ], + "score": 0.83, + "content": "\\epsilon _ { \\pi }", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 500, + 448, + 517 + ], + "score": 1.0, + "content": ". The behavior cloning objective in its supremum form is,", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "interline_equation", + "bbox": [ + 165, + 517, + 445, + 596 + ], + "lines": [ + { + "bbox": [ + 165, + 517, + 445, + 596 + ], + "spans": [ + { + "bbox": [ + 165, + 517, + 445, + 596 + ], + "score": 0.95, + "content": "\\begin{array} { r c l } { { \\epsilon _ { \\beta } } } & { { = } } & { { \\displaystyle \\operatorname* { s u p } _ { s \\in \\mathcal { D } } \\mathbb { E } _ { a \\sim \\mathcal { D } ( - | s ) } [ \\| a - \\hat { \\pi } _ { \\beta } \\left( s \\right) \\| _ { 2 } ^ { 2 } / 2 ] - \\mathcal { H } ( \\pi _ { b } ( - | s ) ) } } \\\\ { { } } & { { } } & { { \\displaystyle = } } & { { \\displaystyle \\operatorname* { s u p } _ { s \\in \\mathcal { D } } \\mathbb { E } _ { a \\sim \\mathcal { D } ( - | s ) } \\left[ - \\log \\pi _ { \\theta _ { 0 } } ( a | s ) \\right] - \\mathcal { H } ( \\pi _ { b } ( - | s ) ) - \\frac { d _ { a } } { 2 } \\log 2 \\pi } } \\\\ { { } } & { { } } & { { \\displaystyle = } } & { { \\displaystyle \\operatorname* { s u p } _ { s \\in \\mathcal { D } } D _ { K L } ( \\pi _ { b } ( - | s ) | | \\pi _ { \\theta _ { 0 } } ( - | s ) ) - \\frac { d _ { a } } { 2 } \\log 2 \\pi . } } \\end{array}", + "type": "interline_equation", + "image_path": "510a7a6f4c53ed1fd9bf08aa7d02a389c968aa539179d59d749e976e7870b259.jpg" + } + ] + } + ], + "index": 31, + "virtual_lines": [ + { + "bbox": [ + 165, + 517, + 445, + 543.3333333333334 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 165, + 543.3333333333334, + 445, + 569.6666666666667 + ], + "spans": [], + "index": 31 + }, + { + "bbox": [ + 165, + 569.6666666666667, + 445, + 596.0000000000001 + ], + "spans": [], + "index": 32 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 598, + 424, + 610 + ], + "lines": [ + { + "bbox": [ + 106, + 597, + 425, + 612 + ], + "spans": [ + { + "bbox": [ + 106, + 597, + 425, + 612 + ], + "score": 1.0, + "content": "We apply Pinsker’s inequality to the true and estimated behavior policy to yield", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "interline_equation", + "bbox": [ + 196, + 613, + 414, + 642 + ], + "lines": [ + { + "bbox": [ + 196, + 613, + 414, + 642 + ], + "spans": [ + { + "bbox": [ + 196, + 613, + 414, + 642 + ], + "score": 0.92, + "content": "\\operatorname* { s u p } _ { s } D _ { T V } ( \\pi _ { b } ( - | s ) | | \\pi _ { \\theta _ { 0 } } ( - | s ) ) \\leq { \\sqrt { { \\frac { 1 } { 2 } } \\epsilon _ { \\beta } + { \\frac { d _ { a } } { 4 } } \\log 2 \\pi } } .", + "type": "interline_equation", + "image_path": "cd03e1a355c462e8c51673a94646e5c30e546ca5516d39be57268f3f2d32018e.jpg" + } + ] + } + ], + "index": 34.5, + "virtual_lines": [ + { + "bbox": [ + 196, + 613, + 414, + 627.5 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 196, + 627.5, + 414, + 642.0 + ], + "spans": [], + "index": 35 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 651, + 279, + 663 + ], + "lines": [ + { + "bbox": [ + 105, + 649, + 280, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 280, + 666 + ], + "score": 1.0, + "content": "By the same Pinsker’s inequality, we have,", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "interline_equation", + "bbox": [ + 217, + 666, + 393, + 689 + ], + "lines": [ + { + "bbox": [ + 217, + 666, + 393, + 689 + ], + "spans": [ + { + "bbox": [ + 217, + 666, + 393, + 689 + ], + "score": 0.91, + "content": "\\operatorname* { s u p } _ { s } D _ { T V } \\big ( \\pi _ { \\theta _ { k } } ( - | s ) | | \\pi _ { \\theta _ { k + 1 } } ( - | s ) \\big ) \\leq \\sqrt { \\delta / 2 } .", + "type": "interline_equation", + "image_path": "cc6a736a77029996a3131bc442a1cd7ba489b5215b67cb069131c1f6b0992f95.jpg" + } + ] + } + ], + "index": 37, + "virtual_lines": [ + { + "bbox": [ + 217, + 666, + 393, + 689 + ], + "spans": [], + "index": 37 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 691, + 275, + 703 + ], + "lines": [ + { + "bbox": [ + 105, + 690, + 275, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 690, + 275, + 705 + ], + "score": 1.0, + "content": "Therefore, by triangle inequality, we have", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "interline_equation", + "bbox": [ + 163, + 707, + 446, + 735 + ], + "lines": [ + { + "bbox": [ + 163, + 707, + 446, + 735 + ], + "spans": [ + { + "bbox": [ + 163, + 707, + 446, + 735 + ], + "score": 0.92, + "content": "\\operatorname* { s u p } _ { s } D _ { T V } ( \\pi _ { b } ( - | s ) | | \\pi _ { \\theta _ { T } } ( - | s ) ) \\leq \\sqrt { \\frac { 1 } { 2 } \\epsilon _ { \\beta } + \\frac { d _ { a } } { 4 } \\log { 2 \\pi } } + T \\sqrt { \\frac { 1 } { 2 } \\delta } = \\epsilon _ { \\pi } ,", + "type": "interline_equation", + "image_path": "adbda65b070ce562bc17233c93098a26063b412526439385966fa8c83b1bd933.jpg" + } + ] + } + ], + "index": 39, + "virtual_lines": [ + { + "bbox": [ + 163, + 707, + 446, + 735 + ], + "spans": [], + "index": 39 + } + ] + } + ], + "page_idx": 13, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 26, + 292, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "score": 1.0, + "content": "14", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 161, + 94 + ], + "lines": [ + { + "bbox": [ + 106, + 81, + 163, + 96 + ], + "spans": [ + { + "bbox": [ + 106, + 81, + 163, + 96 + ], + "score": 1.0, + "content": "APPENDIX", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "title", + "bbox": [ + 107, + 106, + 453, + 121 + ], + "lines": [ + { + "bbox": [ + 105, + 106, + 455, + 122 + ], + "spans": [ + { + "bbox": [ + 105, + 106, + 455, + 122 + ], + "score": 1.0, + "content": "A IMPLICIT KL CONTROL FROM A MATHEMATICAL PERSPECTIVE", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 106, + 131, + 505, + 212 + ], + "lines": [ + { + "bbox": [ + 106, + 132, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 106, + 132, + 505, + 144 + ], + "score": 1.0, + "content": "We can intuitively understand that behavior cloning initialization with trust-region updates works as", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 143, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 505, + 156 + ], + "score": 1.0, + "content": "a regularization of distributional shift, and this can be supported by theory. Following the notation", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 154, + 504, + 166 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 504, + 166 + ], + "score": 1.0, + "content": "of Janner et al. (2019), we denote the generalization error of a dynamics model on the state distribution", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 164, + 506, + 180 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 243, + 180 + ], + "score": 1.0, + "content": "under the true behavior policy as", + "type": "text" + }, + { + "bbox": [ + 244, + 165, + 473, + 179 + ], + "score": 0.91, + "content": "\\begin{array} { r } { \\epsilon _ { m } = \\operatorname* { m a x } _ { t } \\mathbb { E } _ { s \\sim d _ { t } ^ { \\pi _ { b } } } D _ { T V } ( \\bar { p ( } s _ { t + 1 } | s _ { t } , a _ { t } ) | | p _ { \\phi } ( s _ { t + 1 } | s _ { t } , a _ { t } ) ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 474, + 164, + 506, + 180 + ], + "score": 1.0, + "content": ", where", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 177, + 505, + 190 + ], + "spans": [ + { + "bbox": [ + 107, + 178, + 128, + 189 + ], + "score": 0.89, + "content": "D _ { T V }", + "type": "inline_equation" + }, + { + "bbox": [ + 129, + 177, + 372, + 190 + ], + "score": 1.0, + "content": "represents the total variation distance between true dynamics", + "type": "text" + }, + { + "bbox": [ + 372, + 181, + 379, + 189 + ], + "score": 0.76, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 177, + 455, + 190 + ], + "score": 1.0, + "content": "and learned model", + "type": "text" + }, + { + "bbox": [ + 455, + 180, + 467, + 190 + ], + "score": 0.83, + "content": "p _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 467, + 177, + 505, + 190 + ], + "score": 1.0, + "content": ". We also", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 189, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 106, + 189, + 314, + 201 + ], + "score": 1.0, + "content": "denote the distribution shift on the target policy as", + "type": "text" + }, + { + "bbox": [ + 314, + 189, + 413, + 201 + ], + "score": 0.84, + "content": "\\begin{array} { r } { \\operatorname* { m a x } _ { s } D _ { T V } ( \\pi _ { b } | | \\pi ) \\le \\epsilon _ { \\pi } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 414, + 189, + 505, + 201 + ], + "score": 1.0, + "content": ". A bound relating the", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 199, + 499, + 213 + ], + "spans": [ + { + "bbox": [ + 105, + 199, + 154, + 213 + ], + "score": 1.0, + "content": "true returns", + "type": "text" + }, + { + "bbox": [ + 155, + 200, + 173, + 212 + ], + "score": 0.91, + "content": "\\eta [ \\pi ]", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 199, + 263, + 213 + ], + "score": 1.0, + "content": "and the model returns", + "type": "text" + }, + { + "bbox": [ + 263, + 200, + 281, + 212 + ], + "score": 0.95, + "content": "\\hat { \\eta } [ \\pi ]", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 199, + 499, + 213 + ], + "score": 1.0, + "content": "on the target policy is given in Janner et al. (2019) as,", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 132, + 506, + 213 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 202, + 215, + 408, + 243 + ], + "lines": [ + { + "bbox": [ + 202, + 215, + 408, + 243 + ], + "spans": [ + { + "bbox": [ + 202, + 215, + 408, + 243 + ], + "score": 0.92, + "content": "\\eta [ \\pi ] \\ge \\hat { \\eta } [ \\pi ] - \\left[ \\frac { 2 \\gamma r _ { m a x } ( \\epsilon _ { m } + 2 \\epsilon _ { \\pi } ) } { ( 1 - \\gamma ) ^ { 2 } } + \\frac { 4 r _ { m a x } \\epsilon _ { \\pi } } { ( 1 - \\gamma ) } \\right] .", + "type": "interline_equation", + "image_path": "d61ef7ba6dbba742a282990d7b12e361b9ee354446876eed6f9a57f566e8039b.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 202, + 215, + 408, + 243 + ], + "spans": [], + "index": 9 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 245, + 505, + 279 + ], + "lines": [ + { + "bbox": [ + 105, + 244, + 506, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 506, + 258 + ], + "score": 1.0, + "content": "This bound guarantees the improvement under the true returns as long as the improvement under", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 256, + 506, + 268 + ], + "spans": [ + { + "bbox": [ + 105, + 256, + 395, + 268 + ], + "score": 1.0, + "content": "the model returns increases by more than the slack in the bound due to", + "type": "text" + }, + { + "bbox": [ + 395, + 258, + 421, + 268 + ], + "score": 0.9, + "content": "\\epsilon _ { m } , \\epsilon _ { \\pi }", + "type": "inline_equation" + }, + { + "bbox": [ + 422, + 256, + 506, + 268 + ], + "score": 1.0, + "content": "(Janner et al., 2019;", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 266, + 189, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 189, + 279 + ], + "score": 1.0, + "content": "Levine et al., 2020).", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11, + "bbox_fs": [ + 105, + 244, + 506, + 279 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 283, + 505, + 339 + ], + "lines": [ + { + "bbox": [ + 106, + 283, + 505, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 283, + 505, + 297 + ], + "score": 1.0, + "content": "We may relate this bound to the specific learning employed by BREMEN, which includes dynamics", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 294, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 505, + 309 + ], + "score": 1.0, + "content": "model learning, behavior cloning policy initialization, and conservative KL-based trust-region policy", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 305, + 505, + 318 + ], + "spans": [ + { + "bbox": [ + 106, + 305, + 505, + 318 + ], + "score": 1.0, + "content": "updates. To do so, we consider an idealized version of BREMEN, where the expectations over states", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 317, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 505, + 330 + ], + "score": 1.0, + "content": "in equations Equation 1, 3, 4 are replaced with supremums and the dynamics model is set to have", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 329, + 162, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 329, + 162, + 340 + ], + "score": 1.0, + "content": "unit variance.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 15, + "bbox_fs": [ + 105, + 283, + 505, + 340 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 342, + 504, + 365 + ], + "lines": [ + { + "bbox": [ + 106, + 342, + 506, + 355 + ], + "spans": [ + { + "bbox": [ + 106, + 342, + 506, + 355 + ], + "score": 1.0, + "content": "Proposition 1 (Policy and model error bound). Suppose we apply the idealized BREMEN on a", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 352, + 474, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 138, + 367 + ], + "score": 1.0, + "content": "dataset", + "type": "text" + }, + { + "bbox": [ + 138, + 354, + 146, + 363 + ], + "score": 0.77, + "content": "\\mathcal { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 352, + 194, + 367 + ], + "score": 1.0, + "content": ", and define", + "type": "text" + }, + { + "bbox": [ + 195, + 354, + 218, + 366 + ], + "score": 0.88, + "content": "\\epsilon _ { \\beta } , \\epsilon _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 352, + 474, + 367 + ], + "score": 1.0, + "content": "in terms of the behavior cloning and dynamics model losses as,", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 342, + 506, + 367 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 179, + 369, + 432, + 416 + ], + "lines": [ + { + "bbox": [ + 179, + 369, + 432, + 416 + ], + "spans": [ + { + "bbox": [ + 179, + 369, + 432, + 416 + ], + "score": 0.95, + "content": "\\begin{array} { r l } & { \\epsilon _ { \\beta } : = \\underset { s } { \\operatorname* { s u p } } \\mathbb { E } _ { a \\sim \\mathcal { D } ( - | s ) } [ \\| a - \\hat { \\pi } _ { \\beta } \\left( s \\right) \\| _ { 2 } ^ { 2 } / 2 ] - \\mathcal { H } ( \\pi _ { b } ( - | s ) ) } \\\\ & { \\epsilon _ { \\phi } : = \\underset { s , a } { \\operatorname* { s u p } } \\mathbb { E } _ { s ^ { \\prime } \\sim \\mathcal { D } ( - | s , a ) } \\left[ \\| s ^ { \\prime } - \\hat { f } _ { \\phi } ( s , a ) \\| _ { 2 } ^ { 2 } / 2 \\right] - \\mathcal { H } ( p ( - | s , a ) ) , } \\end{array}", + "type": "interline_equation", + "image_path": "c2f2c3d72e588942d1f90e27679108d3e13e651aa575885e47b8e07354fb2315.jpg" + } + ] + } + ], + "index": 21, + "virtual_lines": [ + { + "bbox": [ + 179, + 369, + 432, + 384.6666666666667 + ], + "spans": [], + "index": 20 + }, + { + "bbox": [ + 179, + 384.6666666666667, + 432, + 400.33333333333337 + ], + "spans": [], + "index": 21 + }, + { + "bbox": [ + 179, + 400.33333333333337, + 432, + 416.00000000000006 + ], + "spans": [], + "index": 22 + } + ] + }, + { + "type": "text", + "bbox": [ + 104, + 419, + 505, + 444 + ], + "lines": [ + { + "bbox": [ + 106, + 418, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 106, + 418, + 132, + 432 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 420, + 142, + 429 + ], + "score": 0.78, + "content": "\\mathcal { H }", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 418, + 338, + 432 + ], + "score": 1.0, + "content": "denotes the Shannon entropy. If one then applies", + "type": "text" + }, + { + "bbox": [ + 338, + 420, + 347, + 429 + ], + "score": 0.67, + "content": "T", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 418, + 505, + 432 + ], + "score": 1.0, + "content": "KL-based trust-region steps of step size", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 107, + 430, + 485, + 444 + ], + "spans": [ + { + "bbox": [ + 107, + 433, + 112, + 442 + ], + "score": 0.71, + "content": "\\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 113, + 431, + 348, + 444 + ], + "score": 1.0, + "content": "(Equation 4) using stochastic dynamics models with mean", + "type": "text" + }, + { + "bbox": [ + 348, + 430, + 359, + 444 + ], + "score": 0.9, + "content": "\\hat { f } _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 431, + 455, + 444 + ], + "score": 1.0, + "content": "and standard deviation", + "type": "text" + }, + { + "bbox": [ + 455, + 433, + 461, + 442 + ], + "score": 0.52, + "content": "^ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 461, + 431, + 485, + 444 + ], + "score": 1.0, + "content": ", then", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5, + "bbox_fs": [ + 106, + 418, + 505, + 444 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 172, + 447, + 438, + 476 + ], + "lines": [ + { + "bbox": [ + 172, + 447, + 438, + 476 + ], + "spans": [ + { + "bbox": [ + 172, + 447, + 438, + 476 + ], + "score": 0.94, + "content": "\\epsilon _ { \\pi } = \\sqrt { \\frac { 1 } { 2 } \\epsilon _ { \\beta } + \\frac { d _ { a } } { 4 } \\log 2 \\pi } + T \\sqrt { \\frac { 1 } { 2 } \\delta } ; \\epsilon _ { m } \\leq \\sqrt { \\frac { 1 } { 2 } \\epsilon _ { \\phi } + \\frac { d _ { s } } { 4 } \\log 2 \\pi } ,", + "type": "interline_equation", + "image_path": "8ccdfa3eb115b464fecd2fe3267fdfdd209a81219d9b0a18cf587294a3b2cc52.jpg" + } + ] + } + ], + "index": 26, + "virtual_lines": [ + { + "bbox": [ + 172, + 447, + 438, + 456.6666666666667 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 172, + 456.6666666666667, + 438, + 466.33333333333337 + ], + "spans": [], + "index": 26 + }, + { + "bbox": [ + 172, + 466.33333333333337, + 438, + 476.00000000000006 + ], + "spans": [], + "index": 27 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 479, + 369, + 491 + ], + "lines": [ + { + "bbox": [ + 105, + 477, + 370, + 493 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 133, + 493 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 480, + 144, + 490 + ], + "score": 0.86, + "content": "d _ { a }", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 477, + 163, + 493 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 163, + 479, + 173, + 490 + ], + "score": 0.86, + "content": "d _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 477, + 370, + 493 + ], + "score": 1.0, + "content": "denotes the dimension of action and state space.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28, + "bbox_fs": [ + 105, + 477, + 370, + 493 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 502, + 446, + 514 + ], + "lines": [ + { + "bbox": [ + 105, + 500, + 448, + 517 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 206, + 517 + ], + "score": 1.0, + "content": "Proof. We first consider", + "type": "text" + }, + { + "bbox": [ + 206, + 504, + 216, + 514 + ], + "score": 0.83, + "content": "\\epsilon _ { \\pi }", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 500, + 448, + 517 + ], + "score": 1.0, + "content": ". The behavior cloning objective in its supremum form is,", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 500, + 448, + 517 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 165, + 517, + 445, + 596 + ], + "lines": [ + { + "bbox": [ + 165, + 517, + 445, + 596 + ], + "spans": [ + { + "bbox": [ + 165, + 517, + 445, + 596 + ], + "score": 0.95, + "content": "\\begin{array} { r c l } { { \\epsilon _ { \\beta } } } & { { = } } & { { \\displaystyle \\operatorname* { s u p } _ { s \\in \\mathcal { D } } \\mathbb { E } _ { a \\sim \\mathcal { D } ( - | s ) } [ \\| a - \\hat { \\pi } _ { \\beta } \\left( s \\right) \\| _ { 2 } ^ { 2 } / 2 ] - \\mathcal { H } ( \\pi _ { b } ( - | s ) ) } } \\\\ { { } } & { { } } & { { \\displaystyle = } } & { { \\displaystyle \\operatorname* { s u p } _ { s \\in \\mathcal { D } } \\mathbb { E } _ { a \\sim \\mathcal { D } ( - | s ) } \\left[ - \\log \\pi _ { \\theta _ { 0 } } ( a | s ) \\right] - \\mathcal { H } ( \\pi _ { b } ( - | s ) ) - \\frac { d _ { a } } { 2 } \\log 2 \\pi } } \\\\ { { } } & { { } } & { { \\displaystyle = } } & { { \\displaystyle \\operatorname* { s u p } _ { s \\in \\mathcal { D } } D _ { K L } ( \\pi _ { b } ( - | s ) | | \\pi _ { \\theta _ { 0 } } ( - | s ) ) - \\frac { d _ { a } } { 2 } \\log 2 \\pi . } } \\end{array}", + "type": "interline_equation", + "image_path": "510a7a6f4c53ed1fd9bf08aa7d02a389c968aa539179d59d749e976e7870b259.jpg" + } + ] + } + ], + "index": 31, + "virtual_lines": [ + { + "bbox": [ + 165, + 517, + 445, + 543.3333333333334 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 165, + 543.3333333333334, + 445, + 569.6666666666667 + ], + "spans": [], + "index": 31 + }, + { + "bbox": [ + 165, + 569.6666666666667, + 445, + 596.0000000000001 + ], + "spans": [], + "index": 32 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 598, + 424, + 610 + ], + "lines": [ + { + "bbox": [ + 106, + 597, + 425, + 612 + ], + "spans": [ + { + "bbox": [ + 106, + 597, + 425, + 612 + ], + "score": 1.0, + "content": "We apply Pinsker’s inequality to the true and estimated behavior policy to yield", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33, + "bbox_fs": [ + 106, + 597, + 425, + 612 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 196, + 613, + 414, + 642 + ], + "lines": [ + { + "bbox": [ + 196, + 613, + 414, + 642 + ], + "spans": [ + { + "bbox": [ + 196, + 613, + 414, + 642 + ], + "score": 0.92, + "content": "\\operatorname* { s u p } _ { s } D _ { T V } ( \\pi _ { b } ( - 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To collect multiple data points per experiment and show this trade-off, we run recursive", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 327, + 506, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 506, + 342 + ], + "score": 1.0, + "content": "BREMEN with different batch sizes, and record how many samples are required to cross different", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 340, + 182, + 351 + ], + "spans": [ + { + "bbox": [ + 106, + 340, + 182, + 351 + ], + "score": 1.0, + "content": "reward thresholds.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12.5 + }, + { + "type": "text", + "bbox": [ + 106, + 356, + 506, + 401 + ], + "lines": [ + { + "bbox": [ + 105, + 354, + 506, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 506, + 369 + ], + "score": 1.0, + "content": "HalfCheetah (Reward 7,000 result) and other results from Figure 5 generally show that high deploy-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 367, + 507, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 507, + 380 + ], + "score": 1.0, + "content": "ment efficiency lowers sample efficiency, confirming the inherent trade-off. 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The model dynamics loss is", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1, + "bbox_fs": [ + 105, + 98, + 339, + 113 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 154, + 115, + 455, + 198 + ], + "lines": [ + { + "bbox": [ + 154, + 115, + 455, + 198 + ], + "spans": [ + { + "bbox": [ + 154, + 115, + 455, + 198 + ], + "score": 0.96, + "content": "\\begin{array} { r c l } { { \\epsilon _ { \\phi } } } & { { = } } & { { \\displaystyle \\operatorname* { s u p } _ { s , a } \\mathbb { E } _ { s ^ { \\prime } \\sim \\mathcal { D } ( - | s , a ) } \\left[ \\| s ^ { \\prime } - \\hat { f } _ { \\phi } ( s , a ) \\| _ { 2 } ^ { 2 } / 2 \\right] - \\mathcal { H } ( p ( - | s , a ) ) } } \\\\ { { } } & { { } } & { { } } \\\\ { { \\displaystyle = } } & { { \\displaystyle \\operatorname* { s u p } _ { s , a } \\mathbb { E } _ { s ^ { \\prime } \\sim \\mathcal { D } ( - | s , a ) } \\left[ - \\log p _ { \\phi } ( s ^ { \\prime } | s , a ) \\right] - \\mathcal { H } ( p ( - | s , a ) ) - \\frac { d _ { s } } { 2 } \\log 2 \\pi } } \\\\ { { } } & { { } } & { { } } \\\\ { { \\displaystyle = } } & { { \\displaystyle \\operatorname* { s u p } _ { s , a } D _ { K L } ( p ( - | s , a ) | | p _ { \\phi } ( - | s , a ) ) - \\frac { d _ { s } } { 2 } \\log 2 \\pi . } } \\end{array}", + "type": "interline_equation", + "image_path": "aa87fc6f3057155c6737ed593a8a5dafd8d078ffdb95066df40607dddf37e869.jpg" + } + ] + } + ], + "index": 3, + "virtual_lines": [ + { + "bbox": [ + 154, + 115, + 455, + 142.66666666666666 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 154, + 142.66666666666666, + 455, + 170.33333333333331 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 154, + 170.33333333333331, + 455, + 197.99999999999997 + ], + "spans": [], + "index": 4 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 201, + 421, + 214 + ], + "lines": [ + { + "bbox": [ + 105, + 201, + 420, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 201, + 420, + 215 + ], + "score": 1.0, + "content": "We apply Pinsker’s inequality to the true dynamics and learned model to yield", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 201, + 420, + 215 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 179, + 218, + 431, + 248 + ], + "lines": [ + { + "bbox": [ + 179, + 218, + 431, + 248 + ], + "spans": [ + { + "bbox": [ + 179, + 218, + 431, + 248 + ], + "score": 0.93, + "content": "\\epsilon _ { m } \\leq \\operatorname* { s u p } _ { s , a } D _ { T V } ( p ( - | s , a ) | | p _ { \\phi } ( - | s , a ) ) \\leq \\sqrt { \\frac { 1 } { 2 } \\epsilon _ { \\phi } + \\frac { d _ { s } } { 4 } \\log 2 \\pi } ,", + "type": "interline_equation", + "image_path": "dc340071f12361b39a5e91cdb583922019af7ff05d0a8d67d4402eec2d3f9721.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 179, + 218, + 431, + 228.0 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 179, + 228.0, + 431, + 238.0 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 179, + 238.0, + 431, + 248.0 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 253, + 150, + 265 + ], + "lines": [ + { + "bbox": [ + 105, + 253, + 151, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 151, + 265 + ], + "score": 1.0, + "content": "as desired.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9, + "bbox_fs": [ + 105, + 253, + 151, + 265 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 280, + 451, + 294 + ], + "lines": [ + { + "bbox": [ + 104, + 280, + 453, + 296 + ], + "spans": [ + { + "bbox": [ + 104, + 280, + 453, + 296 + ], + "score": 1.0, + "content": "B TRADE-OFF BETWEEN SAMPLE AND DEPLOYMENT EFFICIENCY", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 106, + 305, + 505, + 350 + ], + "lines": [ + { + "bbox": [ + 105, + 306, + 506, + 319 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 506, + 319 + ], + "score": 1.0, + "content": "An important aspect of deployment efficiency is the trade-off between sample and deployment", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 317, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 505, + 330 + ], + "score": 1.0, + "content": "efficiency. To collect multiple data points per experiment and show this trade-off, we run recursive", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 327, + 506, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 506, + 342 + ], + "score": 1.0, + "content": "BREMEN with different batch sizes, and record how many samples are required to cross different", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 340, + 182, + 351 + ], + "spans": [ + { + "bbox": [ + 106, + 340, + 182, + 351 + ], + "score": 1.0, + "content": "reward thresholds.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12.5, + "bbox_fs": [ + 105, + 306, + 506, + 351 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 356, + 506, + 401 + ], + "lines": [ + { + "bbox": [ + 105, + 354, + 506, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 506, + 369 + ], + "score": 1.0, + "content": "HalfCheetah (Reward 7,000 result) and other results from Figure 5 generally show that high deploy-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 367, + 507, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 507, + 380 + ], + "score": 1.0, + "content": "ment efficiency lowers sample efficiency, confirming the inherent trade-off. 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The numbers above the points (e.g. 1000, 2000, ...) represent the reward threshold.", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 567, + 505, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 567, + 505, + 581 + ], + "score": 1.0, + "content": "The results (especially, reward 7,000 threshold in HalfCheetah) generally show that high deployment efficiency", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 577, + 321, + 589 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 321, + 589 + ], + "score": 1.0, + "content": "lowers sample efficiency, confirming the inherent trade-off.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24.5 + } + ], + "index": 22.25 + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 106, + 81, + 437, + 108 + ], + "lines": [ + { + "bbox": [ + 106, + 81, + 438, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 81, + 438, + 95 + ], + "score": 1.0, + "content": "C DISCUSSION: IMPORTANCE OF DEPLOYMENT EFFICIENCY IN", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 127, + 95, + 282, + 109 + ], + "spans": [ + { + "bbox": [ + 127, + 95, + 282, + 109 + ], + "score": 1.0, + "content": "REAL-WORLD APPLICATIONS", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 107, + 120, + 506, + 164 + ], + "lines": [ + { + "bbox": [ + 105, + 119, + 505, + 132 + ], + "spans": [ + { + "bbox": [ + 105, + 119, + 505, + 132 + ], + "score": 1.0, + "content": "Our notion of deployment-efficiency is necessitated by cost and safety constraints typical in many real", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 130, + 507, + 143 + ], + "spans": [ + { + "bbox": [ + 105, + 130, + 507, + 143 + ], + "score": 1.0, + "content": "world scenarios. Namely, a common approach to real-world applications (Cabi et al., 2020; Dulac-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 141, + 505, + 154 + ], + "spans": [ + { + "bbox": [ + 105, + 141, + 505, + 154 + ], + "score": 1.0, + "content": "Arnold et al., 2019; Kalashnikov et al., 2018) is the following iterative training and data-collection", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 152, + 151, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 152, + 151, + 167 + ], + "score": 1.0, + "content": "paradigm:", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 3.5 + }, + { + "type": "text", + "bbox": [ + 129, + 174, + 505, + 257 + ], + "lines": [ + { + "bbox": [ + 129, + 174, + 334, + 186 + ], + "spans": [ + { + "bbox": [ + 129, + 174, + 334, + 186 + ], + "score": 1.0, + "content": "1. 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Monitor the policy works as expected e.g. checking if it does not violate safety criterion", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 230, + 415, + 242 + ], + "spans": [ + { + "bbox": [ + 141, + 230, + 415, + 242 + ], + "score": 1.0, + "content": "(this safety verification step may alternatively happen before step 3)", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 128, + 243, + 380, + 258 + ], + "spans": [ + { + "bbox": [ + 128, + 243, + 380, + 258 + ], + "score": 1.0, + "content": "5. 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Specifically, Step 4 requires evaluating the policy for safety, and often requires", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 298, + 506, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 506, + 311 + ], + "score": 1.0, + "content": "human monitors (Atkeson et al., 2015). As for Step 3, communication to workers can also be a", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 310, + 506, + 321 + ], + "spans": [ + { + "bbox": [ + 106, + 310, + 506, + 321 + ], + "score": 1.0, + "content": "bottleneck, especially in highly-parallelized distributed RL systems (Nair et al., 2015; Espeholt et al.,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 319, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 506, + 334 + ], + "score": 1.0, + "content": "2018; 2019). Every policy deployment requires a potentially expensive communication between", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 331, + 425, + 343 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 425, + 343 + ], + "score": 1.0, + "content": "different machines/processes, and this can be a bottleneck on the whole system.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 348, + 505, + 469 + ], + "lines": [ + { + "bbox": [ + 106, + 348, + 505, + 361 + ], + "spans": [ + { + "bbox": [ + 106, + 348, + 505, + 361 + ], + "score": 1.0, + "content": "As a concrete example of the necessity of good deployment efficiency, consider optimization of", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 360, + 506, + 372 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 506, + 372 + ], + "score": 1.0, + "content": "personalization in web apps or recommender systems (Abel et al., 2017). 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Accordingly, the deployment-efficiency", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 457, + 348, + 471 + ], + "spans": [ + { + "bbox": [ + 106, + 457, + 348, + 471 + ], + "score": 1.0, + "content": "of any candidate RL algorithm is of tantamount importance.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 474, + 505, + 563 + ], + "lines": [ + { + "bbox": [ + 106, + 475, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 505, + 487 + ], + "score": 1.0, + "content": "The safe exploration might be mentioned as a potential alternative to deployment-efficiency. While", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 484, + 506, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 506, + 499 + ], + "score": 1.0, + "content": "safe exploration can arguably tackle the first concern above (safety risks of the policy), it does nothing", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 497, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 497, + 505, + 509 + ], + "score": 1.0, + "content": "to mitigate the latter (the engineering or communication costs associated with online deployment", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 508, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 505, + 520 + ], + "score": 1.0, + "content": "of a policy). Furthermore, this still ignores the fact that in many scenarios the ability to do safe", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 519, + 506, + 531 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 506, + 531 + ], + "score": 1.0, + "content": "exploration is not a given. While some safe RL algorithms can provide guarantees in tabular cases,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 530, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 106, + 530, + 506, + 542 + ], + "score": 1.0, + "content": "these guarantees no longer hold when using function approximation with neural networks (Chow", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 541, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 541, + 505, + 552 + ], + "score": 1.0, + "content": "et al., 2018). In these cases, it can be much more difficult to perform “safe exploration” than it is to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 552, + 276, + 564 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 276, + 564 + ], + "score": 1.0, + "content": "develop a deployment-efficient algorithm.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33.5 + } + ], + "page_idx": 15, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 292, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 752, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 13 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 106, + 81, + 437, + 108 + ], + "lines": [ + { + "bbox": [ + 106, + 81, + 438, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 81, + 438, + 95 + ], + "score": 1.0, + "content": "C DISCUSSION: IMPORTANCE OF DEPLOYMENT EFFICIENCY IN", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 127, + 95, + 282, + 109 + ], + "spans": [ + { + "bbox": [ + 127, + 95, + 282, + 109 + ], + "score": 1.0, + "content": "REAL-WORLD APPLICATIONS", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 107, + 120, + 506, + 164 + ], + "lines": [ + { + "bbox": [ + 105, + 119, + 505, + 132 + ], + "spans": [ + { + "bbox": [ + 105, + 119, + 505, + 132 + ], + "score": 1.0, + "content": "Our notion of deployment-efficiency is necessitated by cost and safety constraints typical in many real", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 130, + 507, + 143 + ], + "spans": [ + { + "bbox": [ + 105, + 130, + 507, + 143 + ], + "score": 1.0, + "content": "world scenarios. Namely, a common approach to real-world applications (Cabi et al., 2020; Dulac-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 141, + 505, + 154 + ], + "spans": [ + { + "bbox": [ + 105, + 141, + 505, + 154 + ], + "score": 1.0, + "content": "Arnold et al., 2019; Kalashnikov et al., 2018) is the following iterative training and data-collection", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 152, + 151, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 152, + 151, + 167 + ], + "score": 1.0, + "content": "paradigm:", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 3.5, + "bbox_fs": [ + 105, + 119, + 507, + 167 + ] + }, + { + "type": "index", + "bbox": [ + 129, + 174, + 505, + 257 + ], + "lines": [ + { + "bbox": [ + 129, + 174, + 334, + 186 + ], + "spans": [ + { + "bbox": [ + 129, + 174, + 334, + 186 + ], + "score": 1.0, + "content": "1. Aggregate past previous dataset from worker(s)", + "type": "text" + } + ], + "index": 6, + "is_list_start_line": true + }, + { + "bbox": [ + 129, + 189, + 312, + 201 + ], + "spans": [ + { + "bbox": [ + 129, + 189, + 312, + 201 + ], + "score": 1.0, + "content": "2. Update policy based on the collected data", + "type": "text" + } + ], + "index": 7, + "is_list_start_line": true + }, + { + "bbox": [ + 129, + 204, + 281, + 216 + ], + "spans": [ + { + "bbox": [ + 129, + 204, + 281, + 216 + ], + "score": 1.0, + "content": "3. Deploy the policy to the worker(s)", + "type": "text" + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 128, + 218, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 128, + 218, + 505, + 232 + ], + "score": 1.0, + "content": "4. Monitor the policy works as expected e.g. checking if it does not violate safety criterion", + "type": "text" + } + ], + "index": 9, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 230, + 415, + 242 + ], + "spans": [ + { + "bbox": [ + 141, + 230, + 415, + 242 + ], + "score": 1.0, + "content": "(this safety verification step may alternatively happen before step 3)", + "type": "text" + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 128, + 243, + 380, + 258 + ], + "spans": [ + { + "bbox": [ + 128, + 243, + 380, + 258 + ], + "score": 1.0, + "content": "5. Let the worker(s) collect experiences with the latest policy.", + "type": "text" + } + ], + "index": 11, + "is_list_start_line": true + } + ], + "index": 8.5, + "bbox_fs": [ + 128, + 174, + 505, + 258 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 266, + 505, + 343 + ], + "lines": [ + { + "bbox": [ + 104, + 264, + 506, + 279 + ], + "spans": [ + { + "bbox": [ + 104, + 264, + 506, + 279 + ], + "score": 1.0, + "content": "It is easy to see that the number of deployments is a critical bottleneck, as it involves both monitoring", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 277, + 506, + 289 + ], + "spans": [ + { + "bbox": [ + 106, + 277, + 506, + 289 + ], + "score": 1.0, + "content": "of the policy (Step 4) and communication to the workers (Step 3), and both of these steps can incur", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 287, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 287, + 505, + 300 + ], + "score": 1.0, + "content": "significant cost. Specifically, Step 4 requires evaluating the policy for safety, and often requires", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 298, + 506, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 506, + 311 + ], + "score": 1.0, + "content": "human monitors (Atkeson et al., 2015). As for Step 3, communication to workers can also be a", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 310, + 506, + 321 + ], + "spans": [ + { + "bbox": [ + 106, + 310, + 506, + 321 + ], + "score": 1.0, + "content": "bottleneck, especially in highly-parallelized distributed RL systems (Nair et al., 2015; Espeholt et al.,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 319, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 506, + 334 + ], + "score": 1.0, + "content": "2018; 2019). Every policy deployment requires a potentially expensive communication between", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 331, + 425, + 343 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 425, + 343 + ], + "score": 1.0, + "content": "different machines/processes, and this can be a bottleneck on the whole system.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 15, + "bbox_fs": [ + 104, + 264, + 506, + 343 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 348, + 505, + 469 + ], + "lines": [ + { + "bbox": [ + 106, + 348, + 505, + 361 + ], + "spans": [ + { + "bbox": [ + 106, + 348, + 505, + 361 + ], + "score": 1.0, + "content": "As a concrete example of the necessity of good deployment efficiency, consider optimization of", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 360, + 506, + 372 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 506, + 372 + ], + "score": 1.0, + "content": "personalization in web apps or recommender systems (Abel et al., 2017). Once a policy is learned on", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 370, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 506, + 383 + ], + "score": 1.0, + "content": "a batch of past experiences, it is deployed to a collection of web-hosting servers. 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While", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 484, + 506, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 506, + 499 + ], + "score": 1.0, + "content": "safe exploration can arguably tackle the first concern above (safety risks of the policy), it does nothing", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 497, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 497, + 505, + 509 + ], + "score": 1.0, + "content": "to mitigate the latter (the engineering or communication costs associated with online deployment", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 508, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 505, + 520 + ], + "score": 1.0, + "content": "of a policy). Furthermore, this still ignores the fact that in many scenarios the ability to do safe", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 519, + 506, + 531 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 506, + 531 + ], + "score": 1.0, + "content": "exploration is not a given. While some safe RL algorithms can provide guarantees in tabular cases,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 530, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 106, + 530, + 506, + 542 + ], + "score": 1.0, + "content": "these guarantees no longer hold when using function approximation with neural networks (Chow", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 541, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 541, + 505, + 552 + ], + "score": 1.0, + "content": "et al., 2018). In these cases, it can be much more difficult to perform “safe exploration” than it is to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 552, + 276, + 564 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 276, + 564 + ], + "score": 1.0, + "content": "develop a deployment-efficient algorithm.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 475, + 506, + 564 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 106, + 81, + 439, + 94 + ], + "lines": [ + { + "bbox": [ + 105, + 80, + 441, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 441, + 96 + ], + "score": 1.0, + "content": "D EVALUATING OFFLINE PERFORMANCES ON D4RL DATASETS", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 106, + 505, + 227 + ], + "lines": [ + { + "bbox": [ + 105, + 105, + 505, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 119 + ], + "score": 1.0, + "content": "We compare BREMEN to MOPO (Yu et al., 2020), concurrently proposed model-based offline", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 117, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 106, + 117, + 506, + 129 + ], + "score": 1.0, + "content": "methods penalized by model epistemic uncertainty, and state-of-the-art model-free offline algorithms,", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 127, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 104, + 127, + 506, + 141 + ], + "score": 1.0, + "content": "namely, CQL (Kumar et al., 2020), BEAR (Kumar et al., 2019), BRAC (Wu et al., 2019), AWR (Peng", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 138, + 506, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 506, + 151 + ], + "score": 1.0, + "content": "et al., 2019) and BCQ (Fujimoto et al., 2019), on the D4RL MuJoCo locomotion datasets (Fu et al.,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 149, + 505, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 505, + 162 + ], + "score": 1.0, + "content": "2020), used as standard offline RL benchmarks (Kumar et al., 2020; Nair et al., 2020). They have", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 162, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 106, + 162, + 505, + 173 + ], + "score": 1.0, + "content": "several types of offline data collected with different strategies. We choose the hyper parameters of", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 171, + 504, + 184 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 504, + 184 + ], + "score": 1.0, + "content": "BREMEN in Section 5.1 and F.2.2. Table 2 shows BREMEN beats recent state-of-the-art algorithms", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 182, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 505, + 195 + ], + "score": 1.0, + "content": "with the highest normalized score (around 100 corresponds to an expert) in several tasks, while none", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 193, + 505, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 193, + 505, + 206 + ], + "score": 1.0, + "content": "of the methods consistently achieves the best performance. This result suggests that the implicit", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 205, + 506, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 506, + 217 + ], + "score": 1.0, + "content": "regularization with the model-based method performs surprisingly well in offline settings despite of", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 216, + 163, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 163, + 228 + ], + "score": 1.0, + "content": "its simplicity.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 106, + 237, + 523, + 372 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 106, + 237, + 523, + 372 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 237, + 523, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 523, + 372 + ], + "score": 0.983, + "html": "
Task NameBCBREMENMOPOCQLBEARBRAC-vAWRBCQ
halfcheetah-randomwalker2d-randomhopper-random2.11.69.836.93.712.231.913.013.335.47.025.17.311.431.21.912.22.51.510.22.24.910.6
10.8
halfcheetah-mediumwalker2d-mediumhopper-medium36.16.629.055.059.669.340.214.026.544.479.258.041.759.152.146.381.131.137.417.435.940.753.154.5
halfcheetah-medium-replaywalker2d-medium-replayhopper-medium-replay38.411.311.847.27.624.154.042.792.546.238.619.233.747.70.90.640.315.528.438.2
26.748.615.033.1
halfcheetah-medium-expertwalker2d-medium-experthopper-medium-expert35.86.4111.953.355.264.657.955.051.762.498.7111.053.440.196.341.981.60.852.753.827.164.757.5110.9
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BREMEN achieves the best and competitive score", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 406, + 370, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 370, + 417 + ], + "score": 1.0, + "content": "in several domains, while none of the algorithms beats all other methods.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16.5 + } + ], + "index": 14.75 + }, + { + "type": "title", + "bbox": [ + 108, + 439, + 492, + 466 + ], + "lines": [ + { + "bbox": [ + 104, + 438, + 494, + 454 + ], + "spans": [ + { + "bbox": [ + 104, + 438, + 494, + 454 + ], + "score": 1.0, + "content": "E INCORPORATING PESSIMISTIC MODEL-BASED OFFLINE METHODS INTO", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 126, + 453, + 182, + 466 + ], + "spans": [ + { + "bbox": [ + 126, + 453, + 182, + 466 + ], + "score": 1.0, + "content": "BREMEN", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 106, + 478, + 505, + 600 + ], + "lines": [ + { + "bbox": [ + 106, + 479, + 506, + 490 + ], + "spans": [ + { + "bbox": [ + 106, + 479, + 506, + 490 + ], + "score": 1.0, + "content": "The concurrent model-based offline RL methods prescribe the use of uncertainty-based penalties (Ki-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 489, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 505, + 502 + ], + "score": 1.0, + "content": "dambi et al., 2020; Yu et al., 2020), which can be incorporated into BREMEN. We therefore", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 499, + 506, + 514 + ], + "spans": [ + { + "bbox": [ + 104, + 499, + 506, + 514 + ], + "score": 1.0, + "content": "augmented BREMEN with either a hard (MOReL-like, green) or soft (MOPO-like, orange) reward", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 511, + 506, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 506, + 524 + ], + "score": 1.0, + "content": "penalty according to model uncertainty. 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Soft reward", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 104, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 104, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "penalty (MOPO-like, orange) performs well in the environments where the incomplete models appear to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 709, + 138, + 721 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 138, + 721 + ], + "score": 1.0, + "content": "be fatal.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36 + } + ], + "index": 34.5 + } + ], + "page_idx": 16, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 292, + 37 + ], + "lines": [ + { + "bbox": [ + 105, + 25, + 293, + 39 + ], + "spans": [ + { + "bbox": [ + 105, + 25, + 293, + 39 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 310, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 13 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 106, + 81, + 439, + 94 + ], + "lines": [ + { + "bbox": [ + 105, + 80, + 441, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 441, + 96 + ], + "score": 1.0, + "content": "D EVALUATING OFFLINE PERFORMANCES ON D4RL DATASETS", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 106, + 505, + 227 + ], + "lines": [ + { + "bbox": [ + 105, + 105, + 505, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 119 + ], + "score": 1.0, + "content": "We compare BREMEN to MOPO (Yu et al., 2020), concurrently proposed model-based offline", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 117, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 106, + 117, + 506, + 129 + ], + "score": 1.0, + "content": "methods penalized by model epistemic uncertainty, and state-of-the-art model-free offline algorithms,", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 127, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 104, + 127, + 506, + 141 + ], + "score": 1.0, + "content": "namely, CQL (Kumar et al., 2020), BEAR (Kumar et al., 2019), BRAC (Wu et al., 2019), AWR (Peng", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 138, + 506, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 506, + 151 + ], + "score": 1.0, + "content": "et al., 2019) and BCQ (Fujimoto et al., 2019), on the D4RL MuJoCo locomotion datasets (Fu et al.,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 149, + 505, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 505, + 162 + ], + "score": 1.0, + "content": "2020), used as standard offline RL benchmarks (Kumar et al., 2020; Nair et al., 2020). They have", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 162, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 106, + 162, + 505, + 173 + ], + "score": 1.0, + "content": "several types of offline data collected with different strategies. We choose the hyper parameters of", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 171, + 504, + 184 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 504, + 184 + ], + "score": 1.0, + "content": "BREMEN in Section 5.1 and F.2.2. Table 2 shows BREMEN beats recent state-of-the-art algorithms", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 182, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 505, + 195 + ], + "score": 1.0, + "content": "with the highest normalized score (around 100 corresponds to an expert) in several tasks, while none", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 193, + 505, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 193, + 505, + 206 + ], + "score": 1.0, + "content": "of the methods consistently achieves the best performance. This result suggests that the implicit", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 205, + 506, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 506, + 217 + ], + "score": 1.0, + "content": "regularization with the model-based method performs surprisingly well in offline settings despite of", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 216, + 163, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 163, + 228 + ], + "score": 1.0, + "content": "its simplicity.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 6, + "bbox_fs": [ + 104, + 105, + 506, + 228 + ] + }, + { + "type": "table", + "bbox": [ + 106, + 237, + 523, + 372 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 106, + 237, + 523, + 372 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 237, + 523, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 523, + 372 + ], + "score": 0.983, + "html": "
Task NameBCBREMENMOPOCQLBEARBRAC-vAWRBCQ
halfcheetah-randomwalker2d-randomhopper-random2.11.69.836.93.712.231.913.013.335.47.025.17.311.431.21.912.22.51.510.22.24.910.6
10.8
halfcheetah-mediumwalker2d-mediumhopper-medium36.16.629.055.059.669.340.214.026.544.479.258.041.759.152.146.381.131.137.417.435.940.753.154.5
halfcheetah-medium-replaywalker2d-medium-replayhopper-medium-replay38.411.311.847.27.624.154.042.792.546.238.619.233.747.70.90.640.315.528.438.2
26.748.615.033.1
halfcheetah-medium-expertwalker2d-medium-experthopper-medium-expert35.86.4111.953.355.264.657.955.051.762.498.7111.053.440.196.341.981.60.852.753.827.164.757.5110.9
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EnvironmentRewardfunctionTerminationinrollouts
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EnvironmentRewardfunctionTerminationinrollouts
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ParameterAntHalfCheetahHopperWalker2d
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The", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 655, + 303, + 665 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 303, + 665 + ], + "score": 1.0, + "content": "number of transitions per one data-collection is 200K.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26.5 + } + ], + "index": 25.25 + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 505, + 126 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "Stationary Noise in BREMEN To achieve effective exploration, the stochastic Gaussian policy", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 93, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 104, + 93, + 505, + 107 + ], + "score": 1.0, + "content": "is a good choice. We found that adding stationary Gaussian noise to the policy in the imaginary", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 506, + 118 + ], + "score": 1.0, + "content": "trajectories and data collection led to the notable improvement. 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The number of transitions per one", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 397, + 195, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 195, + 408 + ], + "score": 1.0, + "content": "data-collection is 200K.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14.5 + } + ], + "index": 13.25 + }, + { + "type": "text", + "bbox": [ + 106, + 427, + 505, + 494 + ], + "lines": [ + { + "bbox": [ + 106, + 428, + 505, + 439 + ], + "spans": [ + { + "bbox": [ + 106, + 428, + 505, + 439 + ], + "score": 1.0, + "content": "Other Hyper-parameters in the Existing Methods As for online ME-TRPO, we collect 3,000", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 439, + 506, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 506, + 451 + ], + "score": 1.0, + "content": "steps through online interaction with the environment per 25 iterations and split these transitions into", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 450, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 505, + 461 + ], + "score": 1.0, + "content": "a 2-to-1 ratio of training and validation dataset for learning dynamics models. In batch size 100,000", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 459, + 506, + 474 + ], + "spans": [ + { + "bbox": [ + 104, + 459, + 506, + 474 + ], + "score": 1.0, + "content": "settings, we collect 2,000 steps and split with 1-to-1 ratio. Totally, we iterate 12,500 times policy", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "score": 1.0, + "content": "optimization, which is equivalent to 500 deployments of the policy. Note that we carefully tune up", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 482, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 106, + 482, + 506, + 495 + ], + "score": 1.0, + "content": "the hyper-parameters of online ME-TRPO, and the performance is improved from Wang et al. 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ParameterAntHalfCheetahHopperWalker2d
Policy learning rate3e-053e-043e-063e-05
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ParameterAntHalfCheetahHopperWalker2d
Policy learning rate1e-41e-33e-51e-5
Divergence penalty α0.30.10.30.3
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The training curves of each experiment are shown", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 349, + 178, + 361 + ], + "spans": [ + { + "bbox": [ + 106, + 349, + 178, + 361 + ], + "score": 1.0, + "content": "in Appendix G.4.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 326, + 506, + 361 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 373, + 387, + 385 + ], + "lines": [ + { + "bbox": [ + 106, + 373, + 388, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 373, + 388, + 386 + ], + "score": 1.0, + "content": "G.2 COMPARISON AMONG DIFFERENT NUMBER OF ENSEMBLES", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 106, + 394, + 506, + 460 + ], + "lines": [ + { + "bbox": [ + 105, + 393, + 506, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 506, + 406 + ], + "score": 1.0, + "content": "To deal with the distribution shift during policy optimization, also known as model bias, we introduce", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 406, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 505, + 417 + ], + "score": 1.0, + "content": "the dynamics model ensembles. 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Noise: eps1,1,000,000 (1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset10772936791815
BC1381±713788±740266±4861185±155
BCQ1937±1166046±276800±659479±537
BRAC2693±1557003±1181243±1623204±103
BRAC (max Q)2907±987070±811488±3863330±147
BREMEN (Ours)3519±1297585±4252818±761710±429
ME-TRPO (offline)1514±5031009±7311301±654128±153
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MethodAntHalfCheetahHopperWalker2d
Dataset BC BCQ BRAC936 1364±121 1938±21 2718±90 2913±872408 2877±797 5739±188 6434±147662 519±532 1170±446 1224±71648 1066±176 1018±1231 2921±101
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MethodAntHalfCheetahHopperWalker2d
Dataset107231508821070
BC1279±804142±18931±161137±477
BCQ1958±765854±498475±416608±416
BRAC2905±817026±1681456±1613030±103
BRAC (max Q)2910±1577026±1681575±893242±97
BREMEN (Ours)2912±1657928±3131999±6171402±290
ME-TRPO (offline)1275±6561275±656909±631171±119
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Noise:gaussian3,1,0oo,0oo (1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset10582872781981
BC1300±344190±69611±4671217±361
BCQ1982±975781±5431137±582258±286
BRAC3084±1803933±27401432±4993253±118
BRAC (max Q)2916±993997±27611417±2673372±153
BREMEN (Ours)3432±1858124±1451867±3542299±474
ME-TRPO (offline)1237±3102141±872973±243219±145
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MethodAntHalfCheetahHopperWalker2d
Dataset470-285342
BC989±10-2±1106±62108±110
BCQ1222±1142887±242206±7228±12
BRAC1057±923449±259227±3029±54
BRAC (max Q)683±573418±171224±3726±50
BREMEN (Ours)905±113627±193270±68254±6
ME-TRPO (offline)2221±6652701±120321±29262±13
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Noise: eps1,1,000,000 (1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset10772936791815
BC1381±713788±740266±4861185±155
BCQ1937±1166046±276800±659479±537
BRAC2693±1557003±1181243±1623204±103
BRAC (max Q)2907±987070±811488±3863330±147
BREMEN (Ours)3519±1297585±4252818±761710±429
ME-TRPO (offline)1514±5031009±7311301±654128±153
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MethodAntHalfCheetahHopperWalker2d
Dataset BC BCQ BRAC936 1364±121 1938±21 2718±90 2913±872408 2877±797 5739±188 6434±147662 519±532 1170±446 1224±71648 1066±176 1018±1231 2921±101
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MethodAntHalfCheetahHopperWalker2d
Dataset107231508821070
BC1279±804142±18931±161137±477
BCQ1958±765854±498475±416608±416
BRAC2905±817026±1681456±1613030±103
BRAC (max Q)2910±1577026±1681575±893242±97
BREMEN (Ours)2912±1657928±3131999±6171402±290
ME-TRPO (offline)1275±6561275±656909±631171±119
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Noise:gaussian3,1,0oo,0oo (1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset10582872781981
BC1300±344190±69611±4671217±361
BCQ1982±975781±5431137±582258±286
BRAC3084±1803933±27401432±4993253±118
BRAC (max Q)2916±993997±27611417±2673372±153
BREMEN (Ours)3432±1858124±1451867±3542299±474
ME-TRPO (offline)1237±3102141±872973±243219±145
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MethodAntHalfCheetahHopperWalker2d
Dataset470-285342
BC989±10-2±1106±62108±110
BCQ1222±1142887±242206±7228±12
BRAC1057±923449±259227±3029±54
BRAC (max Q)683±573418±171224±3726±50
BREMEN (Ours)905±113627±193270±68254±6
ME-TRPO (offline)2221±6652701±120321±29262±13
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Input: Empty dataset Dau,D,Initial parameters Φ = {1,·,Φk},β,Number of policy optimization T
Numberof deploymentsI.
1:Randomly initialize the target policy πθ .
2:for deploymenti=1,·.,I do
3:Collect B transitions in the true environment using T and add them to dataset
Dall←DalU{St,at,rt,St+1},D←{st,at,rt,St+1}.
4:Train K dynamics models f using Dau via Equation 1.
5: 6:Train estimated behavior policy πβ using D by behavior cloning via Equation 3.
7:Re-initialize target policy πeo = Normal(β,1). for policy optimization k =1,..·,T do
8:Generate imaginary rollout via Equation 2.
9:Optimize target policy Tβ satisfying Equation 4 with the rollout.
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1,000,000(1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset BC1191 1321±141412611281376
4281±12 5783±2721341±161 1130±1271421±147 2153±753
BCQ2021±31 2072±2851422±90
BRAC7192±1152239±1124
BRAC (max Q)2369±2347320±911916±3432409±1210
BREMEN (Ours)3328±2758055±1032058±8522346±230
ME-TRPO (offline)1258±5501804±924518±91211±154
100,000(100K)transitions
MethodAntHalfCheetahHopperWalker2d
Dataset1191406611281376
BC1330±814266±211322±1091426±47
BCQ1363±1993915±4111129±2382187±196
BRAC-157±3832505±25011310±702162±1109
BRAC (max Q)-226±3872332±24221422±1012164±1114
BREMEN (Ours)1633±1276095±3702191±4552132±301
ME-TRPO (offline)974±42±434307±17010±61
50,000 (50K) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset1191413811281376
BC1270±654230±491249±611420±194
BCQ1329±951319±6261178±2351841±439
BRAC-878±244-597±731277±102976±1207
BRAC (max Q)-843±279-590±561276±225903±1137
BREMEN(Ours)1347±2835823±1461632±7962280±647
938±32
ME-TRPO (offfline)-73±95152±13176±343
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Task NameBCBREMENMOPOCQLBEARBRAC-vAWRBCQ
halfcheetah-randomwalker2d-randomhopper-random2.11.69.836.93.712.231.913.013.335.47.025.17.311.431.21.912.22.51.510.22.24.910.6
10.8
halfcheetah-mediumwalker2d-mediumhopper-medium36.16.629.055.059.669.340.214.026.544.479.258.041.759.152.146.381.131.137.417.435.940.753.154.5
halfcheetah-medium-replaywalker2d-medium-replayhopper-medium-replay38.411.311.847.27.624.154.042.792.546.238.619.233.747.70.90.640.315.528.438.2
26.748.615.033.1
halfcheetah-medium-expertwalker2d-medium-experthopper-medium-expert35.86.4111.953.355.264.657.955.051.762.498.7111.053.440.196.341.981.60.852.753.827.164.757.5110.9
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Iteration per batch2,0002,0006.0002,000
Deployment551010
Total iteration10.00010.00060.00020.000
Rollouts length2502501,0001,000
Max step size δ0.050.10.050.05
Discount factor y0.990.990.990.99
GAE入0.970.950.950.95
Stationary noise o0.10.10.10.1
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ParameterAntHalfCheetahHopperWalker2d
Policy learning rate1e-41e-33e-51e-5
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ParameterAntHalfCheetahHopperWalker2d
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MethodAntHalfCheetahHopperWalker2d
Dataset470-285342
BC989±10-2±1106±62108±110
BCQ1222±1142887±242206±7228±12
BRAC1057±923449±259227±3029±54
BRAC (max Q)683±573418±171224±3726±50
BREMEN (Ours)905±113627±193270±68254±6
ME-TRPO (offline)2221±6652701±120321±29262±13
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Noise: eps1,1,000,000 (1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset10772936791815
BC1381±713788±740266±4861185±155
BCQ1937±1166046±276800±659479±537
BRAC2693±1557003±1181243±1623204±103
BRAC (max Q)2907±987070±811488±3863330±147
BREMEN (Ours)3519±1297585±4252818±761710±429
ME-TRPO (offline)1514±5031009±7311301±654128±153
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MethodAntHalfCheetahHopperWalker2d
Dataset BC BCQ BRAC936 1364±121 1938±21 2718±90 2913±872408 2877±797 5739±188 6434±147662 519±532 1170±446 1224±71648 1066±176 1018±1231 2921±101
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MethodAntHalfCheetahHopperWalker2d
Dataset107231508821070
BC1279±804142±18931±161137±477
BCQ1958±765854±498475±416608±416
BRAC2905±817026±1681456±1613030±103
BRAC (max Q)2910±1577026±1681575±893242±97
BREMEN (Ours)2912±1657928±3131999±6171402±290
ME-TRPO (offline)1275±6561275±656909±631171±119
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Noise:gaussian3,1,0oo,0oo (1M) transitions
MethodAntHalfCheetahHopperWalker2d
Dataset10582872781981
BC1300±344190±69611±4671217±361
BCQ1982±975781±5431137±582258±286
BRAC3084±1803933±27401432±4993253±118
BRAC (max Q)2916±993997±27611417±2673372±153
BREMEN (Ours)3432±1858124±1451867±3542299±474
ME-TRPO (offline)1237±3102141±872973±243219±145
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GAUSSIAN ATTENTION MODEL AND ITS APPLICATION TO KNOWLEDGE BASE EMBEDDING AND QUESTION ANSWERING + +Liwen Zhang Department of Computer Science University of Chicago Chicago, IL 60637, USA liwenz@cs.uchicago.edu + +John Winn & Ryota Tomioka Microsoft Research Cambridge Cambridge, CB1 2FB, UK {jwinn, ryoto}@microsoft.com + +# ABSTRACT + +We propose the Gaussian attention model for content-based neural memory access. With the proposed attention model, a neural network has the additional degree of freedom to control the focus of its attention from a laser sharp attention to a broad attention. It is applicable whenever we can assume that the distance in the latent space reflects some notion of semantics. We use the proposed attention model as a scoring function for the embedding of a knowledge base into a continuous vector space and then train a model that performs question answering about the entities in the knowledge base. The proposed attention model can handle both the propagation of uncertainty when following a series of relations and also the conjunction of conditions in a natural way. On a dataset of soccer players who participated in the FIFA World Cup 2014, we demonstrate that our model can handle both path queries and conjunctive queries well. + +# 1 INTRODUCTION + +There is a growing interest in incorporating external memory into neural networks. For example, memory networks (Weston et al., 2014; Sukhbaatar et al., 2015) are equipped with static memory slots that are content or location addressable. Neural Turing machines (Graves et al., 2014) implement memory slots that can be read and written as in Turing machines (Turing, 1938) but through differentiable attention mechanism. + +Each memory slot in these models stores a vector corresponding to a continuous representation of the memory content. In order to recall a piece of information stored in memory, attention is typically employed. Attention mechanism introduced by Bahdanau et al. (2014) uses a network that outputs a discrete probability mass over memory items. A memory read can be implemented as a weighted sum of the memory vectors in which the weights are given by the attention network. Reading out a single item can be realized as a special case in which the output of the attention network is peaked at the desired item. The attention network may depend on the current context as well as the memory item itself. The attention model is called location-based and content-based, if it depends on the location in the memory and the stored memory vector, respectively. + +Knowledge bases, such as WordNet and Freebase, can also be stored in memory either through an explicit knowledge base embedding (Bordes et al., 2011; Nickel et al., 2011; Socher et al., 2013) or through a feedforward network (Bordes et al., 2015). + +When we embed entities from a knowledge base in a continuous vector space, if the capacity of the embedding model is appropriately controlled, we expect semantically similar entities to be close to each other, which will allow the model to generalize to unseen facts. However the notion of proximity may strongly depend on the type of a relation. For example, Benjamin Franklin was an engineer but also a politician. We would need different metrics to capture his proximity to other engineers and politicians of his time. + +![](images/cf5b6abdc7ed89a863d9f6c7b06ccd455538426890860b6ceea74c96c880c10a.jpg) +Figure 1: Comparison of the conventional content-based attention model using inner product and the proposed Gaussian attention model with the same mean but two different covariances. + +In this paper, we propose a new attention model for content-based addressing. Our model scores each item ${ \pmb { v } } _ { \mathrm { i t e m } }$ in the memory by the (logarithm of) multivariate Gaussian likelihood as follows: + +$$ +\begin{array} { r l } & { \mathrm { s c o r e } ( \pmb { v } _ { \mathrm { i t e m } } ) = \log \phi ( \pmb { v } _ { \mathrm { i t e m } } | \pmb { \mu } _ { \mathrm { c o n t e x t } } , \pmb { \Sigma } _ { \mathrm { c o n t e x t } } ) } \\ & { \qquad = - \frac { 1 } { 2 } ( \pmb { v } _ { \mathrm { i t e m } } - \pmb { \mu } _ { \mathrm { c o n t e x t } } ) \pmb { \Sigma } _ { \mathrm { c o n t e x t } } ^ { - 1 } ( \pmb { v } _ { \mathrm { i t e m } } - \pmb { \mu } _ { \mathrm { c o n t e x t } } ) + \mathrm { c o n s t . } } \end{array} +$$ + +where context denotes all the variables that the attention depends on. For example, “American engineers in the $1 8 \mathrm { t h }$ century” or “American politicians in the 18th century” would be two contexts that include Benjamin Franklin but the two attentions would have very different shapes. + +Compared to the (normalized) inner product used in previous work (Sukhbaatar et al., 2015; Graves et al., 2014) for content-based addressing, the Gaussian model has the additional control of the spread of the attention over items in the memory. As we show in Figure 1, we can view the conventional inner-product-based attention and the proposed Gaussian attention as addressing by an affine energy function and a quadratic energy function, respectively. By making the addressing mechanism more complex, we may represent many entities in a relatively low dimensional embedding space. Since knowledge bases are typically extremely sparse, it is more likely that we can afford to have a more complex attention model than a large embedding dimension. + +We apply the proposed Gaussian attention model to question answering based on knowledge bases. At the high-level, the goal of the task is to learn the mapping from a question about objects in the knowledge base in natural language to a probability distribution over the entities. We use the scoring function (1) for both embedding the entities as vectors, and extracting the conditions mentioned in the question and taking a conjunction of them to score each candidate answer to the question. + +The ability to compactly represent a set of objects makes the Gaussian attention model well suited for representing the uncertainty in a multiple-answer question (e.g., “who are the children of Abraham Lincoln?”). Moreover, traversal over the knowledge graph (see Guu et al., 2015) can be naturally handled by a series of Gaussian convolutions, which generalizes the addition of vectors. In fact, we model each relation as a Gaussian with mean and variance parameters. Thus a traversal on a relation corresponds to a translation in the mean and addition of the variances. + +The proposed question answering model is able to handle not only the case where the answer to a question is associated with an atomic fact, which is called simple Q&A (Bordes et al., 2015), but also questions that require composition of relations (path queries in Guu et al. (2015)) and conjunction of queries. An example flow of how our model deals with a question “Who plays forward for Borussia Dortmund?” is shown in Figure 2 in Section 3. + +This paper is structured as follows. In Section 2, we describe how the Gaussian scoring function (1) can be used to embed the entities in a knowledge base into a continuous vector space. We call our model TransGaussian because of its similarity to the TransE model proposed by Bordes et al. (2013). Then in Section 3, we describe our question answering model. In Section 4, we carry out experiments on WorldCup2014 dataset we collected. The dataset is relatively small but it allows us to evaluate not only simple questions but also path queries and conjunction of queries. The proposed TransGaussian embedding with the question answering model achieves significantly higher accuracy than the vanilla TransE embedding or TransE trained with compositional relations Guu et al. (2015) combined with the same question answering model. + +# 2 KNOWLEDGE BASE EMBEDDING + +In this section, we describe the proposed TransGaussian model based on the Gaussian attention model (1). While it is possible to train a network that computes the embedding in a single pass (Bordes et al., 2015) or over multiple passes (Li et al., 2015), it is more efficient to offload the embedding as a separate step for question answering based on a large static knowledge base. + +# 2.1 THE TRANSGAUSSIAN MODEL + +Let $\mathcal { E }$ be the set of entities and $\mathcal { R }$ be the set of relations. A knowledge base is a collection of triplets $( s , r , o )$ , where we call $\textit { s } \in \textit { \varepsilon }$ , $r \in \mathcal { R }$ , and $\textit { o } \in \textit { \mathcal { E } }$ , the subject, the relation, and the object of the triplet, respectively. Each triplet encodes a fact. For example, (Albert Einstein, has profession, theoretical physicist). All the triplets given in a knowledge base are assumed to be true. However generally speaking a triplet may be true or false. Thus knowledge base embedding aims at training a model that predict if a triplet is true or not given some parameterization of the entities and relations (Bordes et al., 2011; 2013; Nickel et al., 2011; Socher et al., 2013; Wang et al., 2014). + +paper, we associate awith two parameters, $\pmb { v } _ { s } \in \mathbb { R } ^ { d }$ with each entity ositive definite s $s \in { \mathcal { E } }$ , and we atric matrix h relation. $r \in \mathcal { R }$ $\pmb { \delta } _ { r } \in \mathbb { R } ^ { d }$ $\pmb { \Sigma } _ { r } \in \mathbb { R } _ { + + } ^ { d \times d }$ + +Given subject $s$ and relation $r$ , we can compute the score of an object $o$ to be in triplet $( s , r , o )$ using the Gaussian attention model as (1) with + +$$ +\begin{array} { r } { \mathrm { s c o r e } ( s , r , o ) = \log \phi ( \pmb { v } _ { o } | \pmb { \mu } _ { \mathrm { c o n t e x t } } , \pmb { \Sigma } _ { \mathrm { c o n t e x t } } ) , } \end{array} +$$ + +where $\pmb { \mu } _ { \mathrm { c o n t e x t } } = \pmb { v } _ { s } + \pmb { \delta } _ { r }$ , $\pmb { \Sigma } _ { \mathrm { c o n t e x t } } = \pmb { \Sigma } _ { r }$ . Note that if $\Sigma _ { r }$ is fixed to the identity matrix, we are modeling the relation of subject ${ \pmb v } _ { s }$ and object ${ \pmb v } _ { o }$ as a translation $\delta _ { r }$ , which is equivalent to the TransE model (Bordes et al., 2013). We allow the covariance $\Sigma _ { r }$ to depend on the relation to handle one-to-many relations (e.g., profession has person relation) and capture the shape of the distribution of the set of objects that can be in the triplet. We call our model TransGaussian because of its similarity to TransE (Bordes et al., 2013). + +Parameterization For computational efficiency, we will restrict the covariance matrix $\Sigma _ { r }$ to be diagonal in this paper. Furthermore, in order to ensure that $\Sigma _ { r }$ is strictly positive definite, we employ the exponential linear unit (ELU, Clevert et al., 2015) and parameterize $\Sigma _ { r }$ as follows: + +$$ +\Sigma _ { r } = \mathrm { d i a g } \left( \begin{array} { c } { { \mathrm { E L U } ( m _ { r , 1 } ) + 1 + \epsilon } } \\ { { } } \\ { { \cdot _ { \cdot _ { \cdot _ { \cdot _ { \cdot _ { \cdot _ { \cdot _ { \cdot _ { \cdot } \cdot _ { \cdot _ { \cdot _ { \cdot } \cdot _ { \cdot _ { \cdot } \cdot _ { \cdot _ { \cdot } \cdot _ { \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot _ { \cdot } \cdot } } } } } } } } } } } } } } } \end{array} \right) +$$ + +where $m _ { r , j } ~ ( j = 1 , \ldots , d )$ are the unconstrained parameters that are optimized during training and $\epsilon$ is a small positive value that ensure the positivity of the variance during numerical computation. The ELU is defined as + +$$ +{ \mathrm { E L U } } ( x ) = { \left\{ \begin{array} { l l } { x , } & { x \geq 0 , } \\ { \exp { ( x ) } - 1 , } & { x < 0 . } \end{array} \right. } +$$ + +Ranking loss Suppose we have a set of triplets $\mathcal { T } = \{ ( s _ { i } , r _ { i } , o _ { i } ) \} _ { i = 1 } ^ { N }$ from the knowledge base. +Let $\mathcal { N } ( s , r )$ be the set of incorrect objects to be in the triplet $( s , r , \cdot )$ . + +Our objective function uses the ranking loss to measure the margin between the scores of true answers and those of false answers and it can be written as follows: + +$$ +\begin{array} { r } { \displaystyle \underset { \{ \delta _ { r } , M _ { r } , : r \in \bar { \mathcal { R } } \} } { \operatorname* { m i n } } \frac { 1 } { N } \sum _ { ( s , r , o ) \in \mathcal { T } } \mathbb { E } _ { t ^ { \prime } \sim \mathcal { N } ( s , r ) } \left[ [ \mu - \mathrm { s c o r e } ( s , r , o ) + \mathrm { s c o r e } ( s , r , t ^ { \prime } ) ] _ { + } \right] } \\ { + \lambda \left( \displaystyle \sum _ { e \in \mathcal { E } } \| v _ { e } \| _ { 2 } ^ { 2 } + \displaystyle \sum _ { r \in \bar { \mathcal { R } } } \big ( \| \delta _ { r } \| _ { 2 } ^ { 2 } + \| M _ { r } \| _ { F } ^ { 2 } \big ) \right) , } \end{array} +$$ + +where, $N = | \mathcal { T } |$ , $\mu$ is the margin parameter and $M _ { r }$ denotes the diagonal matrix with $m _ { r , j } , j =$ $1 , \ldots , d$ on the diagonal; the function $[ \cdot ] _ { + }$ is defined as $[ x ] _ { + } = \operatorname* { m a x } ( 0 , x )$ . Here, we treat an inverse relation as a separate relation and denote by $\bar { \mathcal { R } } = \mathcal { R } \cup \mathcal { R } ^ { - 1 }$ the set of all the relations including both relations in $\mathcal { R }$ and their inverse relations; a relation $\tilde { r }$ is the inverse relation of $r$ if $( s , \tilde { r } , o )$ implies $( o , r , s )$ and vice versa. Moreover, $\mathbb { E } _ { t ^ { \prime } \sim \mathcal { N } ( s , r ) }$ denotes the expectation with respect to the uniform distribution over the set of incorrect objects, which we approximate with 10 random samples in the experiments. Finally, the last terms are $\ell _ { 2 }$ regularization terms for the embedding parameters. + +# 2.2 COMPOSITIONAL RELATIONS + +Guu et al. (2015) has recently shown that training TransE with compositional relations can make it competitive to more complex models, although TransE is much simpler compared to for example, neural tensor networks (NTN, Socher et al. (2013)) and TransH Wang et al. (2014). Here, a compositional relation is a relation that is composed as a series of relations in $\mathcal { R }$ , for example, grand father of can be composed as first applying the parent of relation and then the father of relation, which can be seen as a traversal over a path on the knowledge graph. + +TransGaussian model can naturally handle and propagate the uncertainty over such a chain of relations by convolving the Gaussian distributions along the path. That is, the score of an entity $o$ to be in the $\tau$ -step relation $r _ { 1 } / r _ { 2 } / \cdots / r _ { \tau }$ with subject $s$ , which we denote by the triplet $( \dot { s , } r _ { 1 } / r _ { 2 } / \cdot \cdot \cdot / r _ { \tau } , o )$ , is given as + +$$ +\begin{array} { r } { \mathrm { s c o r e } ( s , r _ { 1 } / r _ { 2 } / \cdot \cdot \cdot / r _ { \tau } , o ) = \log \phi ( \pmb { v } _ { o } | \pmb { \mu } _ { \mathrm { c o n t e x t } } , \pmb { \Sigma } _ { \mathrm { c o n t e x t } } ) , } \end{array} +$$ + +with $\begin{array} { r } { \pmb { \mu } _ { \mathrm { c o n t e x t } } = \pmb { v } _ { s } + \sum _ { t = 1 } ^ { \tau } \delta _ { r _ { t } } } \end{array}$ , $\begin{array} { r } { \sum _ { \mathrm { c o n t e x t } } = \sum _ { t = 1 } ^ { \tau } \sum _ { r _ { t } } } \end{array}$ , where the covariance associated with each relation is parameterized in the same way as in the previous subsection. + +Training with compositional relations Let P = nsi, ri1 /ri2 / · · · /rili , oioN i=1 be a set of randomly sampled paths from the knowledge graph. Here relation $r _ { i _ { k } }$ in a path can be a relation in $\mathcal { R }$ or an inverse relation in $\mathcal { R } ^ { - 1 }$ . With the scoring function (4), the generalized training objective for compositional relations can be written identically to (3) except for replacing $\tau$ with $\mathcal { T } \cup \mathcal { P }$ and replacing $N$ with $N ^ { \prime } = | \mathcal { T } \cup \mathcal { P } |$ . + +# 3 QUESTION ANSWERING + +Given a set of question-answer pairs, in which the question is phrased in natural language and the answer is an entity in the knowledge base, our goal is to train a model that learns the mapping from the question to the correct entity. Our question answering model consists of three steps, entity recognition, relation composition, and conjunction. We first identify a list of entities mentioned in the question (which is assumed to be provided by an oracle in this paper). If the question is “Who plays Forward for Borussia Dortmund?” then the list would be [Forward, Borussia Dortmund]. The next step is to predict the path of relations on the knowledgegraph starting from each entity in the list extracted in the first step. In the above example, this will be (smooth versions of) /Forward/position played by/ and /Borussia Dortmund/has player/ predicted as series of Gaussian convolutions. In general, we can have multiple relations appearing in each path. Finally, we take a product of all the Gaussian attentions and renormalize it, which is equivalent to Bayes’ rule with independent observations (paths) and a noninformative prior. + +# 3.1 ENTITY RECOGNITION + +We assume that there is an oracle that provides a list containing all the entities mentioned in the question, because (1) a domain specific entity recognizer can be developed efficiently (Williams et al., 2015) and (2) generally entity recognition is a challenging task and it is beyond the scope of this paper to show whether there is any benefit in training our question answering model jointly with a entity recognizer. We assume that the number of extracted entities can be different for each question. + +# 3.2 RELATION COMPOSITION + +We train a long short-term memory (LSTM, Hochreiter & Schmidhuber, 1997) network that emits an output $\boldsymbol { h } _ { t }$ for each token in the input sequence. Then we compute the attention over the hidden + +![](images/c8be4c487573afc71d590a3b723235da8f6bd144ebef356a786893ec5f627b32.jpg) +Figure 2: The input to the system is a question in natural language. Two entities Forward and Borussia Dortmund are identified in the question and associated with point mass distributions centered at the corresponding entity vectors. An LSTM encodes the input into a sequence of output vectors of the same length. Then we take average of the output vectors weighted by attention $\mathit { p } _ { t , e }$ for each recognized entity $e$ to predict the weight $\alpha _ { r , e }$ for relation $r$ associated with entity $e$ . We form a Gaussian attention over the entities for each entity $e$ by convolving the corresponding point mass with the (pre-trained) Gaussian embeddings of the relations weighted by $\alpha _ { r , e }$ according to Eq. (6). The final prediction is produced by taking the product and normalizing the Gaussian attentions. + +states for each recognized entity $e$ as + +$$ +p _ { t , e } = \mathrm { s o f t m a x } \left( f ( v _ { e } , h _ { t } ) \right) \quad ( t = 1 , . . . , T ) , +$$ + +where ${ \pmb v } _ { e }$ is the vector associated with the entity $e$ . We use a two-layer perceptron for $f$ in our experiments, which can be written as follows: + +$$ +f ( \pmb { v } _ { e } , \pmb { h } _ { t } ) = \pmb { u } _ { f } ^ { \top } \mathrm { R e L U } \left( \pmb { W } _ { f , v } \pmb { v } _ { e } + \pmb { W } _ { f , h } \pmb { h } _ { t } + \pmb { b } _ { 1 } \right) + b _ { 2 } , +$$ + +where $\mathbf { \widetilde { \Gamma } } _ { f , v } \in \mathbb { R } ^ { L \times d } , W _ { f , h } \in \mathbb { R } ^ { L \times H } , b _ { 1 } \in \mathbb { R } ^ { L } , { \mathbf { u } } _ { f } \in \mathbb { R } ^ { L } , b _ { 2 } \in \mathbb { R } \mathrm { a r e } \mathrm { p a r }$ ameters. Here ${ \mathrm { R e L U } } ( x ) =$ $\operatorname* { m a x } ( 0 , x )$ is the rectified linear unit. Finally, softmax denotes softmax over the $T$ tokens. + +Next, we use the weights $\mathit { p } _ { t , e }$ to compute the weighted sum over the hidden states $\boldsymbol { h } _ { t }$ as + +$$ +o _ { e } = \sum _ { t = 1 } ^ { T } p _ { t , e } h _ { t } . +$$ + +Then we compute the weights $\alpha _ { r , e }$ over all the relations as $\alpha _ { r , e } = \mathrm { R e L U } \left( \pmb { w } _ { r } ^ { \top } \pmb { o } _ { e } \right) \quad \left( \forall r \in \mathcal { R } \cup \right.$ $\mathcal { R } ^ { - 1 }$ ). Here the rectified linear unit is used to ensure the positivity of the weights. Note however that the weights should not be normalized, because we may want to use the same relation more than once in the same path. Making the weights positive also has the effect of making the attention sparse and interpretable because there is no cancellation. + +For each extracted entity $e$ , we view the extracted entity and the answer of the question to be the subject and the object in some triplet $( e , p , o )$ , respectively, where the path $p$ is inferred from the question as the weights $\alpha _ { r , e }$ as we described above. Accordingly, the score for each candidate answer $o$ can be expressed using (1) as: + +$$ +\mathrm { s c o r e } _ { e } ( \pmb { v } _ { o } ) = \log \phi ( \pmb { v } _ { o } | \pmb { \mu } _ { e , \alpha , \mathrm { K B } } , \pmb { \Sigma } _ { e , \alpha , \mathrm { K B } } ) +$$ + +with $\begin{array} { r } { \pmb { \mu } _ { e , \alpha , \mathrm { K B } } = \pmb { v } _ { e } + \sum _ { r \in \bar { \mathcal { R } } } \alpha _ { r , e } \delta _ { r } , \sum _ { e , \alpha , \mathrm { K B } } = \sum _ { r \in \bar { \mathcal { R } } } \alpha _ { r , e } ^ { 2 } \pmb { \Sigma } _ { r } } \end{array}$ , where ${ \pmb v } _ { e }$ is the vector associated with entity $e$ and $\bar { \mathcal { R } } = \mathcal { R } \cup \mathcal { R } ^ { - 1 }$ denotes the set of relations including the inverse relations. + +# 3.3 CONJUNCTION + +Let $\mathcal { E } ( q )$ be the set of entities recognized in the question $q$ . The final step of our model is to take the conjunction of the Gaussian attentions derived in the previous step. This step is simply carried out by multiplying the Gaussian attentions as follows: + +$$ +\begin{array} { r l } & { \mathrm { s c o r e } ( \pmb { v } _ { o } | \mathcal { E } ( q ) , \Theta ) = \underset { e \in \mathcal { E } ( q ) } { \log \prod } \phi ( \pmb { v } _ { o } | \pmb { \mu } _ { e , \alpha , \mathrm { K B } } , \pmb { \Sigma } _ { e , \alpha , \mathrm { K B } } ) } \\ & { \qquad = - \cfrac { 1 } { 2 } \displaystyle \sum _ { e \in \mathcal { E } ( q ) } \left( \pmb { v } _ { o } - \pmb { \mu } _ { e , \alpha , \mathrm { K B } } \right) ^ { \top } \pmb { \Sigma } _ { e , \alpha , \mathrm { K B } } ^ { - 1 } ( \pmb { v } _ { o } - \pmb { \mu } _ { e , \alpha , \mathrm { K B } } ) + \mathrm { c o n s t . } , } \end{array} +$$ + +which is again a (logarithm of) Gaussian scoring function, where $\mu _ { e , \alpha , \mathrm { K B } }$ and $\Sigma _ { e , \alpha , \mathrm { K B } }$ are the mean and the covariance of the Gaussian attention given in (6). Here $\Theta$ denotes all the parameters of the question-answering model. + +# 3.4 TRAINING THE QUESTION ANSWERING MODEL + +Suppose we have a knowledge base $( \mathcal { E } , \mathcal { R } , \mathcal { T } )$ and a trained TransGaussian model $\big ( \{ v _ { e } \} _ { e \in \mathcal { E } } , \{ ( \delta _ { r } , \Sigma _ { r } ) \} _ { r \in \bar { \mathcal { R } } } \big )$ , where $\bar { \mathcal { R } }$ is the set of all relations including the inverse relations. During training time, we assume the training set is a supervised question-answer pairs $\{ ( q _ { i } , \mathcal { E } ( q _ { i } ) , a _ { i } \bar { ) } : i = 1 , 2 , . . . , m \}$ . Here, $q _ { i }$ is a question formulated in natural language, $\bar { \mathcal { E } } ( q _ { i } ) \subset \mathcal { E }$ is a set of knowledge base entities that appears in the question, and $a _ { i } ~ \in { \mathcal { E } }$ is the answer to the question. For example, on a knowledge base of soccer players, a valid training sample could be + +(“Who plays forward for Borussia Dortmund?”,[Forward, Borussia Dortmund], Marco Reus). + +Note that the answer to a question is not necessarily unique and we allow $a _ { i }$ to be any of the true answers in the knowledge base. During test time, our model is shown $\left( q _ { i } , \mathcal { E } ( q _ { i } ) \right)$ and the task is to find $a _ { i }$ . We denote the set of answers to $q _ { i }$ by $A ( q _ { i } )$ . + +To train our question-answering model, we minimize the objective function + +$$ +\frac { 1 } { n } \sum _ { i = 1 } ^ { m } \biggl ( \underset { t ^ { \prime } \sim \mathcal { N } ( q _ { i } ) } { \mathbb { E } } \left[ [ \mu - \mathrm { s c o r e } ( v _ { a _ { i } } | \mathcal { E } ( q _ { i } ) , \Theta ) + \mathrm { s c o r e } ( v _ { t ^ { \prime } } | \mathcal { E } ( q _ { i } ) , \Theta ) ] _ { + } \right] + \nu \sum _ { e \in \mathcal { E } ( q _ { i } ) } \sum _ { r \in \mathcal { R } } | \alpha _ { r , e } | \biggr ) + \lambda \| \Theta \| _ { 2 } ^ { 2 } +$$ + +where $\mathbb { E } _ { t ^ { \prime } \sim \mathcal { N } ( q _ { i } ) }$ is expectation with respect to a uniform distribution over of all incorrect answers to $q _ { i }$ , which we approximate with 10 random samples. We assume that the number of relations implied in a question is small compared to the total number of relations in the knowledge base. Hence the coefficients $\alpha _ { r , e }$ computed for each question $q _ { i }$ are regularized by their $\ell _ { 1 }$ norms. + +# 4 EXPERIMENTS + +As a demonstration of the proposed framework, we perform question and answering on a dataset of soccer players. In this work, we consider two types of questions. A path query is a question that contains only one named entity from the knowledge base and its answer can be found from the knowledge graph by walking down a path consisting of a few relations. A conjunctive query is a question that contains more than one entities and the answer is given as the conjunction of all path queries starting from each entity. Furthermore, we experimented on a knowledge base completion task with TransGaussian embeddings to test its capability of generalization to unseen fact. Since knowledge base completion is not the main focus of this work, we include the results in the Appendix. + +# 4.1 WORLDCUP2014 DATASET + +We build a knowledge base of football players that participated in FIFA World Cup 2014 1. The original dataset consists of players’ information such as nationality, positions on the field and ages etc. We picked a few attributes and constructed 1127 entities and 6 atomic relations. The entities include 736 players, 297 professional soccer clubs, 51 countries, 39 numbers and 4 positions. And the six atomic relations are plays in club: PLAYER $ \mathrm { C L U B }$ , is aged: PLAYER NUMBER, plays for country: PLAYER COUNTRY, plays position: PLAYER POSITION, wears number 2: PLAYER NUMBER, is in country: CLUB COUNTRY, + +where PLAYER, CLUB, NUMBER, etc, denote the type of entities that can appear as the left or right argument for each relation. Some relations share the same type as the right argument, e.g., plays for country and is in country. + +Given the entities and relations, we transformed the dataset into a set of 3977 triplets. A list of sample triplets can be found in the Appendix. Based on these triplets, we created two sets of question answering tasks which we call path query and conjunctive query respectively. The answer of every question is always an entity in the knowledge base and a question can involve one or two triplets. The questions are generated as follows. + +Path queries. Among the paths on the knowledge graph, there are some natural composition of relations, e.g., plays in country (PLAYER COUNTRY) can be decomposed as the composition of plays in club (PLAYE $\mathbf { R } \to \mathbf { C L } $ UB) and is in country $( \mathbf { C L U B } \to \mathbf { C O U N T R Y } )$ . In addition to the atomic relations, we manually picked a few meaningful compositions of relations and formed query templates, which takes the form “find $e \in { \mathcal { E } }$ , such that $( s , p , e )$ is true”, where $s$ is the subject and $p$ can be an atomic relation or a path of relations. To formulate a set of path-based question-answer pairs, we manually created one or more question templates for every query template (see Table 5) Then, for a particular instantiation of a query template with subject and object entities, we randomly select a question template to generate a question given the subject; the object entity becomes the answer of the question. See Table 6 for the list of composed relations, sample questions, and answers. Note that all atomic relations in this dataset are many-to-one while these composed relations can be one-to-many or many-to-many as well. + +Conjunctive queries. To generate question-and-answer pairs of conjunctive queries, we first picked three pairs of relations and used them to create query templates of the form “Find $e \in { \mathcal { E } }$ , such that both $( s _ { 1 } , r _ { 1 } , e )$ and $( s _ { 2 } , r _ { 2 } , e )$ are true.” (see Table 5). For a pair of relations $r _ { 1 }$ and $r _ { 2 }$ , we enumerated all pairs of entities $s _ { 1 } , s _ { 2 }$ that can be their subjects and formulated the corresponding query in natural language using question templates as in the same way as path queries. See Table 7 for a list of sample questions and answers. + +As a result, we created 8003 question-and-answer pairs of path queries and 2208 pairs of conjunctive queries which are partitioned into train / validation $/$ test subsets. We refer to Table 1 for more statistics about the dataset. Templates for generating the questions are list in Table 5. + +# 4.2 EXPERIMENTAL SETUP + +To perform question and answering under our proposed framework, we first train the TransGaussian model on WorldCup2014 dataset. In addition to the atomic triplets, we randomly sampled 50000 paths with length 1 or 2 from the knowledge graph and trained a TransGaussian model compositionally as described in Set 2.2. An inverse relation is treated as a separate relation. Following the naming convention from Guu et al. (2015), we denote this trained embedding by TransGaussian (COMP). We found that the learned embedding possess some interesting properties. Some dimensions of the embedding space dedicate to represent a particular relation. Players are clustered by their attributes when entities’ embeddings are projected to the corresponding lower dimensional subspaces. We elaborate and illustrate such properties in the Appendix. + +Baseline methods We also trained a TransGaussian model only on the atomic triplets and denote such a model by TransGaussian (SINGLE). Since no inverse relation was involved when TransGaussian (SINGLE) was trained, to use this embedding in question answering tasks, we represent the inverse relations as follows: for each relation $r$ with mean $\delta _ { r }$ and variance $\Sigma _ { r }$ , we model its inverse $r ^ { - 1 }$ as a Gaussian attention with mean $- \delta _ { r }$ and variance equal to $\Sigma _ { r }$ . + +We also trained TransE models on WorldCup2014 dataset by using the code released by the authors of Guu et al. (2015). Likewise, we use TransE (SINGLE) to denote the model trained with atomic triplets only and use TransE (COMP) to denote the model trained with the union of triplets and paths. Note that TransE can be considered as a special case of TransGaussian where the variance matrix is the identity and hence, the scoring formula Eq. (7) is applicable to TransE as well. + +Training configurations For all models, dimension of entity embeddings was set to 30. The hidden size of LSTM was set to 80. Word embeddings were trained jointly with the question answering model and dimension of word embedding was set to 40. We employed Adam (Kingma & Ba, 2014) as the optimizer. All parameters were tuned on the validation set. Under the same setting, we experimented with two cases: first, we trained models for path queries and conjunctive queries separately; Furthermore, we trained a single model that addresses both types queries. We present the results of the latter case in the next subsection while the results of the former are included in the Appendix. + +Evaluation metrics During test time, our model receives a question in natural language and a list of knowledge base entities contained in the question. Then it predicts the mean and variance of a Gaussian attention formulated in Eq. (7) which is expected to capture the distribution of all positive answers. We rank all entities in the knowledge base by their scores under this Gaussian attention. Next, for each entity which is a correct answer, we check its rank relative to all incorrect answers and call this rank the filtered rank. For example, if a correct entity is ranked above all negative answers except for one, it has filtered rank two. We compute this rank for all true answers and report mean filtered rank and $H @ l$ which is the percentage of true answers that have filtered rank 1. + +# 4.3 EXPERIMENTAL RESULTS + +We present the results of joint learning in Table 2. These results show that TransGaussian works better than TransE in general. In fact, TransGaussian (COMP) achieved the best performance in almost all aspects. Most notably, it achieved the highest $\mathrm { H @ 1 }$ rates on challenging questions such as “where is the club that edin dzeko plays for?” (#11, composition of two relations) and “who are the defenders on german national team?” (#14, conjunction of two queries). + +The same table shows that TransGaussian benefits remarkably from compositional training. For example, compositional training improved TransGaussian’s $\mathrm { H @ 1 }$ rate by near $60 \%$ in queries on players from a given countries (#8) and queries on players who play a particular position (#9). It also boosted TransGaussian’s performance on all conjunctive quries (#13–#15) significantly. + +To understand TransGaussian (COMP)’s weak performance on answering queries on the professional football club located in a given country (#10) and queries on professional football club that has players from a particular country (#12), we tested its capability of modeling the composed relation by feeding the correct relations and subjects during test time. It turns out that these two relations were not modeled well by TransGaussian (COMP) embedding, which limits its performance in question answering. (See Table 8 in the Appendix for quantitative evaluations.) The same limit was found in the other three embeddings as well. + +Note that all the models compared in Table 2 uses the proposed Gaussian attention model because TransE is the special case of TransGaussian where the variance is fixed to one. Thus the main differences are whether the variance is learned and whether the embedding was trained compositionally. Finally, we refer to Table 9 and 10 in the Appendix for experimental results of models trained on path and conjunctive queries separately. + +Table 1: Some statistics of the WorldCup2014 dataset. + +
# entity
#atomic relations# atomic triplets
# path query Q&A（train/validation/test）# conjunctive query Q&A（train /validation /test）
1127639775620/804/15791564/224/420
+ +# 5 RELATED WORK + +The work of Vilnis & McCallum (2014) is similar to our Gaussian attention model. They discuss many advantages of the Gaussian embedding; for example, it is arguably a better way of handling asymmetric relations and entailment. However the work was presented in the word2vec (Mikolov et al., 2013)-style word embedding setting and the Gaussian embedding was used to capture the diversity in the meaning of a word. Our Gaussian attention model extends their work to a more general setting in which any memory item can be addressed through a concept represented as a Gaussian distribution over the memory items. + +Table 2: Results of joint learning with path queries and conjunction queries on WorldCup2014. + +
TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#Sample questionH@1(%）FilteredMean RankH@1(%）FilteredMean RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered Rank
1which club does alan pulido play for?88.591.1891.951.1196.641.0498.661.01
2what position does gonzalo higuain play?100.001.0098.111.0398.741.01100.001.00
3how old is samuel etoo?67.111.4490.791.1394.741.0897.371.04
4what is the jersey number of mario balotelli?45.001.8983.571.2297.141.0399.291.01
5which country is thomas mueller from ?94.401.0694.401.0696.801.0498.401.02
6which country is the soccer team fc porto based in ?98.481.0298.481.0293.941.0695.451.05
7who plays professionally at liverpool fc?95.121.1090.241.2098.371.0496.751.04
8which player is from iran?89.861.5176.812.0738.652.9699.521.00
9name a player who plays goalkeeper?98.961.0169.791.8242.715.52100.001.00
10which soccer club is based in mexico?22.0313.9430.518.846.7810.6616.9521.14
11where is the club that edin dzeko plays for ？52.633.8857.242.1047.372.2778.291.41
12name a soccer club that has a player from australia ?30.4312.0833.7011.4713.0411.6419.5717.57
Overall (Path Query)74.163.1177.392.5669.543.0285.943.52
13who plays forward for fc barcelona?97.551.0676.071.6693.251.2498.771.02
14who are the defenders on german national team?95.931.0669.922.3365.042.04100.001.00
15which player in ssc napoli is from argentina?88.811.1776.121.7688.811.3597.761.03
Overall(Conj. Query)94.291.0974.291.8983.571.5198.811.02
+ +Bordes et al. (2014; 2015) proposed a question-answering model that embeds both questions and their answers to a common continuous vector space. Their method in Bordes et al. (2015) can combine multiple knowledge bases and even generalize to a knowledge base that was not used during training. However their method is limited to the simple question answering setting in which the answer of each question associated with a triplet in the knowledge base. In contrast, our method can handle both composition of relations and conjunction of conditions, which are both naturally enabled by the proposed Gaussian attention model. + +Neelakantan et al. (2015a) proposed a method that combines relations to deal with compositional relations for knowledge base completion. Their key technical contribution is to use recurrent neural networks (RNNs) to encode a chain of relations. When we restrict ourselves to path queries, question answering can be seen as a sequence transduction task (Graves, 2012; Sutskever et al., 2014) in which the input is text and the output is a series of relations. If we use RNNs as a decoder, our model would be able to handle non-commutative composition of relations, which the current weighted convolution cannot handle well. Another interesting connection to our work is that they take the maximum of the inner-product scores (see also Weston et al., 2013; Neelakantan et al., 2015b), which are computed along multiple paths connecting a pair of entities. Representing a set as a collection of vectors and taking the maximum over the inner-product scores is a natural way to represent a set of memory items. The Gaussian attention model we propose in this paper, however, has the advantage of differentiability and composability. + +# 6 CONCLUSION + +In this paper, we have proposed the Gaussian attention model which can be used in a variety of contexts where we can assume that the distance between the memory items in the latent space is compatible with some notion of semantics. We have shown that the proposed Gaussian scoring function can be used for knowledge base embedding achieving competitive accuracy. We have also shown that our embedding model can naturally propagate uncertainty when we compose relations together. Our embedding model also benefits from compositional training proposed by Guu et al. (2015). Furthermore, we have demonstrated the power of the Gaussian attention model in a challenging question answering problem which involves both composition of relations and conjunction of queries. Future work includes experiments on natural question answering datasets and end-to-end training including the entity extractor. + +# ACKNOWLEDGMENTS + +The authors would like to thank Daniel Tarlow, Nate Kushman, and Kevin Gimpel for valuable discussions. + +# REFERENCES + +Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv:1409.0473, 2014. + +Antoine Bordes, Jason Weston, Ronan Collobert, and Yoshua Bengio. Learning structured embeddings of knowledge bases. In Conference on Artificial Intelligence, number EPFL-CONF-192344, 2011. + +Antoine Bordes, Nicolas Usunier, Alberto Garcia-Duran, Jason Weston, and Oksana Yakhnenko. Translating embeddings for modeling multi-relational data. In Advances in Neural Information Processing Systems, pp. 2787–2795, 2013. + +Antoine Bordes, Jason Weston, and Nicolas Usunier. Open question answering with weakly supervised embedding models. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pp. 165–180. Springer, 2014. + +Antoine Bordes, Nicolas Usunier, Sumit Chopra, and Jason Weston. Large-scale simple question answering with memory networks. arXiv preprint arXiv:1506.02075, 2015. + +Djork-Arne Clevert, Thomas Unterthiner, and Sepp Hochreiter. Fast and accurate deep network´ learning by exponential linear units (elus). arXiv preprint arXiv:1511.07289, 2015. + +Alex Graves. Sequence transduction with recurrent neural networks. arXiv preprint arXiv:1211.3711, 2012. + +Alex Graves, Greg Wayne, and Ivo Danihelka. Neural turing machines. arXiv preprint arXiv:1410.5401, 2014. + +Kelvin Guu, John Miller, and Percy Liang. Traversing knowledge graphs in vector space. In EMNLP 2015, 2015. + +Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8): 1735–1780, 1997. + +Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. + +Yujia Li, Daniel Tarlow, Marc Brockschmidt, and Richard Zemel. Gated graph sequence neural networks. arXiv preprint arXiv:1511.05493, 2015. + +Tomas Mikolov, Kai Chen, Greg Corrado, and Jeffrey Dean. Efficient estimation of word representations in vector space. arXiv preprint arXiv:1301.3781, 2013. + +Arvind Neelakantan, Benjamin Roth, and Andrew McCallum. Compositional vector space models for knowledge base completion. arXiv preprint arXiv:1504.06662, 2015a. + +Arvind Neelakantan, Jeevan Shankar, Alexandre Passos, and Andrew McCallum. Efficient non-parametric estimation of multiple embeddings per word in vector space. arXiv preprint arXiv:1504.06654, 2015b. + +Maximilian Nickel, Volker Tresp, and Hans-Peter Kriegel. A three-way model for collective learning on multi-relational data. In Proceedings of the 28th international conference on machine learning (ICML-11), pp. 809–816, 2011. + +Richard Socher, Danqi Chen, Christopher D Manning, and Andrew Ng. Reasoning with neural tensor networks for knowledge base completion. In Advances in Neural Information Processing Systems, pp. 926–934, 2013. + +Sainbayar Sukhbaatar, Jason Weston, Rob Fergus, et al. End-to-end memory networks. In Advances in neural information processing systems, pp. 2440–2448, 2015. + +Ilya Sutskever, Oriol Vinyals, and Quoc V Le. Sequence to sequence learning with neural networks. In Advances in neural information processing systems, pp. 3104–3112, 2014. + +Alan Mathison Turing. On computable numbers, with an application to the entscheidungsproblem: A correction. Proceedings of the London Mathematical Society, 2(1):544, 1938. + +Luke Vilnis and Andrew McCallum. Word representations via gaussian embedding. arXiv preprint arXiv:1412.6623, 2014. + +Zhen Wang, Jianwen Zhang, Jianlin Feng, and Zheng Chen. Knowledge graph embedding by translating on hyperplanes. In AAAI, pp. 1112–1119. Citeseer, 2014. + +Jason Weston, Ron J Weiss, and Hector Yee. Nonlinear latent factorization by embedding multiple user interests. In Proceedings of the 7th ACM conference on Recommender systems, pp. 65–68. ACM, 2013. + +Jason Weston, Sumit Chopra, and Antoine Bordes. Memory networks. arXiv preprint arXiv:1410.3916, 2014. + +Jason D Williams, Eslam Kamal, Hani Amr Mokhtar Ashour, Jessica Miller, and Geoff Zweig. Fast and easy language understanding for dialog systems with microsoft language understanding intelligent service (LUIS). In 16th Annual Meeting of the Special Interest Group on Discourse and Dialogue, pp. 159, 2015. + +# A WORDCUP2014 DATASET + +Table 3: Sample atomic triplets. + +
SubjectRelationObject
david_villaplays-for_countryspain
lionel_messiplays_in-clubfc_barcelona
antoine-griezmannplays-positionforward
cristiano_ronaldowears_number7
fulham_fcis_in_countryengland
lukas_podolskiis_aged29
+ +Table 4: Statistics of the WorldCup2014 dataset. + +
#entity# atomic relations# atomic triplets112763977
#relations (atomic and compositional) in path queries# question and answer pairs in path queries(train/validation/ test）125620/804/1579
# types of questions in conjunctive queries# question and answer pairs in conjunctive queries(train/validation/test )31564/224/420
size of vocabulary1781
+ +Table 5: Templates of questions. In the table, (player), (club), (position) are placeholders of named entities with associated type. (country 1) is a placeholder for a country name while (country 2) is a placeholder for the adjectival form of a country. + +
#Query templateQuestion template
1Finde ∈ε:((player),plays_in_club,e)is truewhich club does (player) play for ?which professional football team does (player) play for ?which football club does (player) play for ?
2Finde∈ε:(player),plays-position,e)is truewhat position does (player) play ?
3Find e ∈ε:(player),is-aged,e) is truehow old is (player) ?what is the age of (player) ?
4Finde∈ε:(player),wears_number,e) is truewhat is the jersey number of (player) ?what number does (player) wear ?
5Finde ∈ε:(player),plays_for_country,e) is truewhat is the nationality of (player) ?which national team does (player) play for ?which country is (player) from ?
6Finde∈ε:(club),is-in_country,e)is truewhich country is the soccer team (club) based in ?
7Finde ∈ε: (club),plays_in_club-1,e)is truename a player from (club) ?who plays at the soccer club (club) ?who is from the professional football team (club) ?who plays professionally at (club) ?
8Finde ∈ε:(country-1),plays_for-country-1,e)is truewhich player is from (country_1) ?name a player from (country-1) ?who is from (country-1) ?who plays for the (country_1) national football team ?
9Finde∈ε:(position),playsposition-,e)is truename a player who plays (position) ?who plays (position) ?
10Finde ∈ε:(cotry-1),sicountry-1,e)is truewhich soccer club is based in (country_1) ?name a soccer club in (country_1) ?
11Finde∈ε:(player),plays_in_club /is_in_country,e)is truewhich country does (player) play professionally in ?where is the football club that (player) plays for ?
12Finde ∈ε:(country-1),plays-for-country-1/plays_in_club,e)is truewhich professional football team do players from (country_1) play for ？name a soccer club that has a player from (country_1) ?which professional football team has a player from (country_1) ?
13Find e∈ ε:(position),plays-position-1,e) is true and((club),plays-in_club-1,e) is truewho plays (position) for (club)?who are the (position) at (club) ?name a (position) that plays for (club) ?
14Find e∈ε: (position),plays-position-1,e) is true and(country-l),plays-for-country-1,e)is truewho plays (position) for (country_1) ?who are the (position) on (country_1) national team ?name a (position) from (country-1) ?which (country_2) footballer plays (position) ?name a (country-2) (position) ?
15Find e∈ε:(club)， plays_in_club-1,e) is true and(country_l),plays_for_country-1,e)is truewho are the (country_2) playersat (club)？which (country_2) footballer plays for (club) ?name a (country_2) player at (club) ?which player in (club) is from (country-1) ?
+ +Table 6: (Composed) relations and sample questions in path queries. + +
#RelationTypeSample questionSample answer
1plays_in_clubmany-to-onewhich club doesalan pulido play for ?which professional footbal team does klaas jan huntelar play for ?tigres_uanlfc_schalke_04
2plays-positionmany-to-onewhat position does gonzalo higuain play ?ssc_napoli
3is_agedmany-to-onehow old is samuel etoo ?what is the age of luis suarez ?3
4wears-numbermany-to-onewhat is the jersey number of mario balotelli ?what number does shinji okazaki wear ?：
5plays_for_countrymany-to-onewhich country is thomas mueller from ?what is the nationality of helder postiga ?germanyportugal
6is.in_countrymany-to-onewhich country is the soccer team fc porto based in ?portugal
7plays_in_club-1one-to-manywho playsprofessionally at liverpool fc ?name a player from as roma ?steven_gerrardmiralem_pjanic
8plays-for_country-1one-to-manywhich player is from iran ？name a player from italy ?masoud_shojaeidaniele_de_rossi
9plays-position-1one-to-manyname a player who plays goalkeeper ?who plays forward ?gianluiqi-buffonraul_jimenez
10is_in-country-1one-to-manywhich soccer club is based in mexico ?name a soccer club in australia ?cruz_azul.fcmelbourne_victory_fc
11plays_in_club /is_in_countrymany-to-onewhere is the club that edin dzeko plays for ?which country does sime vrsaljko play professionally in ?englanditaly
12plays-for_country-1/plays_in_clubmany-to-manyname a soccer club that has a player from australia?name a soccer club that has a player from spain ?crystal_palace_fcfc_barcelona
+ +Table 7: Conjunctive queries and sample questions. + +
#RelationsSample questionsEntities in questionsSampleanswer
13plays_position-1 and plays_in_club-1who plays forward for fc barcelona ? who are the midfielders at fc bayern muenchen ?forward,fc_barcelona midfielder,fc_bayern_muenchenlionel_messi toni_kroos
14plays-position -1 andwho are the defenders on german national team ? which mexican footballer plays forward ?defender,germany defender,mexicoper_mertesacker raul-jimenez
15plays_in_club-1 and plays_for_country -1which player in paris saint-germain fc is from argentina ? who are the korean players at beijing guoan ?paris_saint-germain_fc,argentina beijing-guoan,koreaezequiel_lavezzi ha-daesung
+ +# B TRANSGAUSSIAN EMBEDDING OF WORLDCUP2014 + +We trained our TransGaussian model on triplets and paths from WorldCup2014 dataset and illustrated the embeddings in Fig 3 and 4. Recall that we modeled every relation as a Gaussian with diagonal covariance matrix. Fig 3 shows the learned variance parameters of different relations. Each row corresponds to the variances of one relation. Columns are permuted to reveal the block structure. From this figure, we can see that every relation has a small variance in two or more dimensions. This implies that the coordinates of the embedding space are partitioned into semantically coherent clusters each of which represent a particular attribute of a player (or a football club). To verify this further, we picked the two coordinates in which a relation (e.g. plays position) has the least variance and projected the embedding of all valid subjects and objects (e.g. players and positions) of the relation to this 2 dimensional subspace. See Fig. 4. The relation between the subjects and the objects are simply translation in the projection when the corresponding subspace is two dimensional (e.g., plays position relation in Fig. 4 (a)). The same is true for other relations that requires larger dimension but it is more challenging to visualize in two dimensions. For relations that have a large number of unique objects, we only plotted for the eight objects with the most subjects for clarity of illustration. + +Furthermore, in order to elucidate whether we are limited by the capacity of the TransGaussian embedding or the ability to decode question expressed in natural language, we evaluated the test question-answer pairs using the TransGaussian embedding composed according to the ground-truth relations and entities. The results were evaluated with the same metrics as in Sec. 4.3. This estimation is conducted for TransE embeddings as well. See Table 8 for the results. Compared to Table 2, the accuracy of TransGaussian (COMP) is higher on the atomic relations and path queries but lower on conjunctive queries. This is natural because when the query is simple there is not much room for the question-answering network to improve upon just combining the relations according to the ground truth relations, whereas when the query is complex the network could combine the embedding in a more creative way to overcome its limitation. In fact, the two queries (#10 and #12) that TransGaussian (COMP) did not perform well in Table 2 pertain to a single relation is in country−1 (#10) and a composition of two relations plays for country $^ - 1 \ /$ plays in club (#12). The performance of the two queries were low even when the ground truth + +![](images/dcac266cd0111b767c6f604dadfa93e9478ad13210e7862e4fc0a7fbd0595157.jpg) +Figure 3: Variance of each relation. Each row shows the diagonal values in the variance matrix associated with a relation. Columns are permuted to reveal the block structure. + +Table 8: Evaluation of embeddings. We evaluate the embeddings by feeding the correct entities and relations from a path or conjunctive query to an embedding model and using its scoring function to retrieve the answers from the embedded knowledge base. + +
TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#RelationH@1(%)Mean Filtered RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered Rank
1plays.in.club75.541.3893.481.0999.861.0098.511.02
2plays-position96.331.0494.021.0998.371.02100.001.00
3is_aged55.031.6991.441.1296.881.03100.001.00
4wears_number38.862.0978.671.3295.921.04100.001.00
5plays_for_country71.601.3994.841.1099.321.01100.001.00
6is_in_country98.321.0399.661.0099.331.01100.001.00
7plays_in_club-187.501.4683.421.4594.701.0797.421.03
882.471.6868.213.3725.275.6698.781.02
9plays-position-1100.001.0075.541.6013.5924.3598.781.02
10is_in-country-123.1126.9223.4823.278.32130.5919.4183.61
11plays_in_club/is_in-country20.247.0558.291.9846.882.9980.161.38
12plays-for_country -1/plays-in_club25.3222.2727.7310.0419.0435.5920.1533.01
Overall(Path relations) plays-position-164.645.0975.023.5967.2214.8786.738.79
13and plays-in_club-1 plays-position91.851.2069.971.8277.451.8395.381.06
14and plays_in_club =T91.711.2366.712.8551.494.8897.831.05
15and is_in_country -188.591.2073.37 70.021.80 2.1683.421.3494.701.08
Overall (Conj.relations)90.721.2170.792.6895.971.06
+ +relations were given, which indicates that the TransGaussian embedding rather than the questionanswering network is the limiting factor. + +# C KNOWLEDGE BASE COMPLETION + +Knowledge base completion has been a common task for testing knowledge base models on their ability of generalizing to unseen facts. Here, we apply our TransGaussian model to a knowledge completion task and show that it has competitive performance. + +We tested on the subset of WordNet released by Guu et al. (2015). The atomic triplets in this dataset was originally created by Socher et al. (2013) and Guu et al. (2015) added path queries that were randomly sampled from the knowledge graph. We build our TransGaussian model by training on these triplets and paths and tested our model on the same link prediction task as done by Socher et al. (2013); Guu et al. (2015). + +As done by Guu et al. (2015), we trained TransGaussian (SINGLE) with atomic triplets only and trained TransGaussian (COMP) with the union of atomic triplets and paths. We did not incorporate word embedding in this task and each entity is assigned its individual vector. Without getting parameters tuned too much, TransGaussian (COMP) obtained accuracy comparable to TransE (COMP). See Table 11. + +![](images/4a25b8273f36037ebd611825cf1990cec4dc4df993551c3f676718009d7fca5b.jpg) +Figure 4: TransGaussian entity embeddings. Crosses are the subjects and circles are the objects of a relation. Specifically, crosses are players in (a)-(e) and professional football clubs in (f). + +Table 9: Experimental results of path queries on WorldCup2014. + +
TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#Relation and sample questionMean H@1(%）Filtered RankH@1(%)Mean Filtered RankMean H@1(%) Filtered RankH@1(%)Mean Filtered Rank
1plays.in_club (which club does alan pulido play for?)90.60 1.1292.621.1196.64 1.0397.991.03
2plays-position (what position does gonzalo higuain play?)100.00 1.0098.111.0298.74 1.01100.001.00
3is_aged (how old is samuel etoo?)81.58 1.3092.111.1096.05 1.04100.001.00
4wears_number (what is the jersey number of mario balotelli?)44.29 1.8885.711.1996.43 1.04100.001.00
5plays-for-country (which country is thomas mueller from ?)97.60 1.0294.401.1198.40 1.0299.201.01
6is_in.country (which country is the soccer team fc porto based in ?)98.48 1.0298.481.0293.94 1.0898.481.02
7plays_in_club-1 (who plays professionally at liverpool fc?)95.12 1.0886.991.3896.75 1.0396.751.03
8plays_for_country (which player is from iran?)81.16 1.6172.462.3640.58 3.1993.241.48
9plays-position (name a player who plays goalkeeper?)100.00 1.0030.212.3055.21 5.0985.421.15
10is.in_country (which soccer club is based in mexico?)24.58 11.4723.7310.075.08 9.1817.8020.10
11plays_in_club/is_in_country (where is the club that edin dzeko plays for ?)48.68 4.2462.502.0748.03 2.4176.971.50
12plays-for-country-1/plays-in-club (name a soccer club that hasaplayer from australia ?)34.78 9.4930.4311.266.52 9.8816.3020.27
Overall74.92 2.8074.352.7170.172.82 84.423.68
+ +Table 10: Experimental results of conjunctive queries on WorldCup2014. + +
TransE(SINGLE)TransE(COMP)TransGaussian(SINGLE)TransGaussian(COMP)
#Relation and sample questionMeanH@1(%)FilteredRankMeanH@1(%)FilteredRankMeanH@1(%)FilteredRankMeanH@1(%)FilteredRank
13(who plays forward for fc barcelona?)94.48 1.1071.17 1.7787.12 1.3798.77 1.02
14plays-position-and plays-for-country-1(who are the defenders on german national team?)95.93 1.0876.42 2.5064.23 2.02100.00 1.00
15plays_in_club-1andis_in_country(which player in ssc napoli is from argentina?)91.79 1.1375.37 1.7588.06 1.3794.03 1.07
Overall94.05 1.1174.05 1.9780.71 1.5697.62 1.03
+ +Table 11: Accuracy of knowledge base completion on WordNet. + +
ModelAccuracy (%)
TransE (SINGLE)68.5
TransE (COMP)80.3
TransGaussian (SINGLE)58.4
TransGaussian (COMP)76.4
\ No newline at end of file diff --git a/parse/train/ByC7ww9le/ByC7ww9le_content_list.json b/parse/train/ByC7ww9le/ByC7ww9le_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..0842b642126ac12d04bae73795154293b715922f --- /dev/null +++ b/parse/train/ByC7ww9le/ByC7ww9le_content_list.json @@ -0,0 +1,1778 @@ +[ + { + "type": "text", + "text": "GAUSSIAN ATTENTION MODEL AND ITS APPLICATION TO KNOWLEDGE BASE EMBEDDING AND QUESTION ANSWERING ", + "text_level": 1, + "bbox": [ + 174, + 98, + 823, + 171 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Liwen Zhang Department of Computer Science University of Chicago Chicago, IL 60637, USA liwenz@cs.uchicago.edu ", + "bbox": [ + 183, + 195, + 403, + 265 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "John Winn & Ryota Tomioka Microsoft Research Cambridge Cambridge, CB1 2FB, UK {jwinn, ryoto}@microsoft.com ", + "bbox": [ + 482, + 195, + 754, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 301, + 544, + 316 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose the Gaussian attention model for content-based neural memory access. With the proposed attention model, a neural network has the additional degree of freedom to control the focus of its attention from a laser sharp attention to a broad attention. It is applicable whenever we can assume that the distance in the latent space reflects some notion of semantics. We use the proposed attention model as a scoring function for the embedding of a knowledge base into a continuous vector space and then train a model that performs question answering about the entities in the knowledge base. The proposed attention model can handle both the propagation of uncertainty when following a series of relations and also the conjunction of conditions in a natural way. On a dataset of soccer players who participated in the FIFA World Cup 2014, we demonstrate that our model can handle both path queries and conjunctive queries well. ", + "bbox": [ + 233, + 338, + 764, + 505 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 545, + 336, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There is a growing interest in incorporating external memory into neural networks. For example, memory networks (Weston et al., 2014; Sukhbaatar et al., 2015) are equipped with static memory slots that are content or location addressable. Neural Turing machines (Graves et al., 2014) implement memory slots that can be read and written as in Turing machines (Turing, 1938) but through differentiable attention mechanism. ", + "bbox": [ + 174, + 582, + 823, + 651 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Each memory slot in these models stores a vector corresponding to a continuous representation of the memory content. In order to recall a piece of information stored in memory, attention is typically employed. Attention mechanism introduced by Bahdanau et al. (2014) uses a network that outputs a discrete probability mass over memory items. A memory read can be implemented as a weighted sum of the memory vectors in which the weights are given by the attention network. Reading out a single item can be realized as a special case in which the output of the attention network is peaked at the desired item. The attention network may depend on the current context as well as the memory item itself. The attention model is called location-based and content-based, if it depends on the location in the memory and the stored memory vector, respectively. ", + "bbox": [ + 174, + 659, + 825, + 784 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Knowledge bases, such as WordNet and Freebase, can also be stored in memory either through an explicit knowledge base embedding (Bordes et al., 2011; Nickel et al., 2011; Socher et al., 2013) or through a feedforward network (Bordes et al., 2015). ", + "bbox": [ + 176, + 791, + 821, + 833 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "When we embed entities from a knowledge base in a continuous vector space, if the capacity of the embedding model is appropriately controlled, we expect semantically similar entities to be close to each other, which will allow the model to generalize to unseen facts. However the notion of proximity may strongly depend on the type of a relation. For example, Benjamin Franklin was an engineer but also a politician. We would need different metrics to capture his proximity to other engineers and politicians of his time. ", + "bbox": [ + 174, + 840, + 825, + 922 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cf5b6abdc7ed89a863d9f6c7b06ccd455538426890860b6ceea74c96c880c10a.jpg", + "image_caption": [ + "Figure 1: Comparison of the conventional content-based attention model using inner product and the proposed Gaussian attention model with the same mean but two different covariances. " + ], + "image_footnote": [], + "bbox": [ + 336, + 97, + 661, + 183 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a new attention model for content-based addressing. Our model scores each item ${ \\pmb { v } } _ { \\mathrm { i t e m } }$ in the memory by the (logarithm of) multivariate Gaussian likelihood as follows: ", + "bbox": [ + 174, + 268, + 823, + 299 + ], + "page_idx": 1 + }, + { + "type": "equation", + "img_path": "images/35303e12d200b6ebe304e88c74e84013ec500365fb64381d5e4d7d6f620b9df6.jpg", + "text": "$$\n\\begin{array} { r l } & { \\mathrm { s c o r e } ( \\pmb { v } _ { \\mathrm { i t e m } } ) = \\log \\phi ( \\pmb { v } _ { \\mathrm { i t e m } } | \\pmb { \\mu } _ { \\mathrm { c o n t e x t } } , \\pmb { \\Sigma } _ { \\mathrm { c o n t e x t } } ) } \\\\ & { \\qquad = - \\frac { 1 } { 2 } ( \\pmb { v } _ { \\mathrm { i t e m } } - \\pmb { \\mu } _ { \\mathrm { c o n t e x t } } ) \\pmb { \\Sigma } _ { \\mathrm { c o n t e x t } } ^ { - 1 } ( \\pmb { v } _ { \\mathrm { i t e m } } - \\pmb { \\mu } _ { \\mathrm { c o n t e x t } } ) + \\mathrm { c o n s t . } } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 238, + 318, + 759, + 369 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where context denotes all the variables that the attention depends on. For example, “American engineers in the $1 8 \\mathrm { t h }$ century” or “American politicians in the 18th century” would be two contexts that include Benjamin Franklin but the two attentions would have very different shapes. ", + "bbox": [ + 176, + 387, + 821, + 429 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compared to the (normalized) inner product used in previous work (Sukhbaatar et al., 2015; Graves et al., 2014) for content-based addressing, the Gaussian model has the additional control of the spread of the attention over items in the memory. As we show in Figure 1, we can view the conventional inner-product-based attention and the proposed Gaussian attention as addressing by an affine energy function and a quadratic energy function, respectively. By making the addressing mechanism more complex, we may represent many entities in a relatively low dimensional embedding space. Since knowledge bases are typically extremely sparse, it is more likely that we can afford to have a more complex attention model than a large embedding dimension. ", + "bbox": [ + 173, + 435, + 825, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We apply the proposed Gaussian attention model to question answering based on knowledge bases. At the high-level, the goal of the task is to learn the mapping from a question about objects in the knowledge base in natural language to a probability distribution over the entities. We use the scoring function (1) for both embedding the entities as vectors, and extracting the conditions mentioned in the question and taking a conjunction of them to score each candidate answer to the question. ", + "bbox": [ + 174, + 554, + 825, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The ability to compactly represent a set of objects makes the Gaussian attention model well suited for representing the uncertainty in a multiple-answer question (e.g., “who are the children of Abraham Lincoln?”). Moreover, traversal over the knowledge graph (see Guu et al., 2015) can be naturally handled by a series of Gaussian convolutions, which generalizes the addition of vectors. In fact, we model each relation as a Gaussian with mean and variance parameters. Thus a traversal on a relation corresponds to a translation in the mean and addition of the variances. ", + "bbox": [ + 173, + 631, + 825, + 715 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The proposed question answering model is able to handle not only the case where the answer to a question is associated with an atomic fact, which is called simple Q&A (Bordes et al., 2015), but also questions that require composition of relations (path queries in Guu et al. (2015)) and conjunction of queries. An example flow of how our model deals with a question “Who plays forward for Borussia Dortmund?” is shown in Figure 2 in Section 3. ", + "bbox": [ + 174, + 722, + 825, + 791 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper is structured as follows. In Section 2, we describe how the Gaussian scoring function (1) can be used to embed the entities in a knowledge base into a continuous vector space. We call our model TransGaussian because of its similarity to the TransE model proposed by Bordes et al. (2013). Then in Section 3, we describe our question answering model. In Section 4, we carry out experiments on WorldCup2014 dataset we collected. The dataset is relatively small but it allows us to evaluate not only simple questions but also path queries and conjunction of queries. The proposed TransGaussian embedding with the question answering model achieves significantly higher accuracy than the vanilla TransE embedding or TransE trained with compositional relations Guu et al. (2015) combined with the same question answering model. ", + "bbox": [ + 173, + 797, + 825, + 924 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 KNOWLEDGE BASE EMBEDDING ", + "text_level": 1, + "bbox": [ + 176, + 102, + 475, + 118 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we describe the proposed TransGaussian model based on the Gaussian attention model (1). While it is possible to train a network that computes the embedding in a single pass (Bordes et al., 2015) or over multiple passes (Li et al., 2015), it is more efficient to offload the embedding as a separate step for question answering based on a large static knowledge base. ", + "bbox": [ + 174, + 132, + 825, + 189 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1 THE TRANSGAUSSIAN MODEL ", + "text_level": 1, + "bbox": [ + 176, + 205, + 424, + 219 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathcal { E }$ be the set of entities and $\\mathcal { R }$ be the set of relations. A knowledge base is a collection of triplets $( s , r , o )$ , where we call $\\textit { s } \\in \\textit { \\varepsilon }$ , $r \\in \\mathcal { R }$ , and $\\textit { o } \\in \\textit { \\mathcal { E } }$ , the subject, the relation, and the object of the triplet, respectively. Each triplet encodes a fact. For example, (Albert Einstein, has profession, theoretical physicist). All the triplets given in a knowledge base are assumed to be true. However generally speaking a triplet may be true or false. Thus knowledge base embedding aims at training a model that predict if a triplet is true or not given some parameterization of the entities and relations (Bordes et al., 2011; 2013; Nickel et al., 2011; Socher et al., 2013; Wang et al., 2014). ", + "bbox": [ + 173, + 231, + 825, + 344 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "paper, we associate awith two parameters, $\\pmb { v } _ { s } \\in \\mathbb { R } ^ { d }$ with each entity ositive definite s $s \\in { \\mathcal { E } }$ , and we atric matrix h relation. $r \\in \\mathcal { R }$ $\\pmb { \\delta } _ { r } \\in \\mathbb { R } ^ { d }$ $\\pmb { \\Sigma } _ { r } \\in \\mathbb { R } _ { + + } ^ { d \\times d }$ ", + "bbox": [ + 174, + 349, + 821, + 381 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given subject $s$ and relation $r$ , we can compute the score of an object $o$ to be in triplet $( s , r , o )$ using the Gaussian attention model as (1) with ", + "bbox": [ + 174, + 387, + 823, + 415 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/5c69bcc35098be68af1a430bd4cb7dbc1fecdbf4ab8b68d54743d74cd3859f79.jpg", + "text": "$$\n\\begin{array} { r } { \\mathrm { s c o r e } ( s , r , o ) = \\log \\phi ( \\pmb { v } _ { o } | \\pmb { \\mu } _ { \\mathrm { c o n t e x t } } , \\pmb { \\Sigma } _ { \\mathrm { c o n t e x t } } ) , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 343, + 420, + 653, + 438 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pmb { \\mu } _ { \\mathrm { c o n t e x t } } = \\pmb { v } _ { s } + \\pmb { \\delta } _ { r }$ , $\\pmb { \\Sigma } _ { \\mathrm { c o n t e x t } } = \\pmb { \\Sigma } _ { r }$ . Note that if $\\Sigma _ { r }$ is fixed to the identity matrix, we are modeling the relation of subject ${ \\pmb v } _ { s }$ and object ${ \\pmb v } _ { o }$ as a translation $\\delta _ { r }$ , which is equivalent to the TransE model (Bordes et al., 2013). We allow the covariance $\\Sigma _ { r }$ to depend on the relation to handle one-to-many relations (e.g., profession has person relation) and capture the shape of the distribution of the set of objects that can be in the triplet. We call our model TransGaussian because of its similarity to TransE (Bordes et al., 2013). ", + "bbox": [ + 173, + 440, + 825, + 525 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Parameterization For computational efficiency, we will restrict the covariance matrix $\\Sigma _ { r }$ to be diagonal in this paper. Furthermore, in order to ensure that $\\Sigma _ { r }$ is strictly positive definite, we employ the exponential linear unit (ELU, Clevert et al., 2015) and parameterize $\\Sigma _ { r }$ as follows: ", + "bbox": [ + 173, + 540, + 823, + 582 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/c1f66c1aa79eb2d4fe7c09b566a6b78148df32593e7806c2db3ed991658d7829.jpg", + "text": "$$\n\\Sigma _ { r } = \\mathrm { d i a g } \\left( \\begin{array} { c } { { \\mathrm { E L U } ( m _ { r , 1 } ) + 1 + \\epsilon } } \\\\ { { } } \\\\ { { \\cdot _ { \\cdot _ { \\cdot _ { \\cdot _ { \\cdot _ { \\cdot _ { \\cdot _ { \\cdot _ { \\cdot } \\cdot _ { \\cdot _ { \\cdot _ { \\cdot } \\cdot _ { \\cdot _ { \\cdot } \\cdot _ { \\cdot _ { \\cdot } \\cdot _ { \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot _ { \\cdot } \\cdot } } } } } } } } } } } } } } } \\end{array} \\right)\n$$", + "text_format": "latex", + "bbox": [ + 334, + 585, + 663, + 631 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $m _ { r , j } ~ ( j = 1 , \\ldots , d )$ are the unconstrained parameters that are optimized during training and $\\epsilon$ is a small positive value that ensure the positivity of the variance during numerical computation. The ELU is defined as ", + "bbox": [ + 174, + 635, + 825, + 676 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/3d40bd351af026f629f9cacb330837b022c4d0c1d9ab8ed13b6d474e7cdb411a.jpg", + "text": "$$\n{ \\mathrm { E L U } } ( x ) = { \\left\\{ \\begin{array} { l l } { x , } & { x \\geq 0 , } \\\\ { \\exp { ( x ) } - 1 , } & { x < 0 . } \\end{array} \\right. }\n$$", + "text_format": "latex", + "bbox": [ + 379, + 680, + 617, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Ranking loss Suppose we have a set of triplets $\\mathcal { T } = \\{ ( s _ { i } , r _ { i } , o _ { i } ) \\} _ { i = 1 } ^ { N }$ from the knowledge base. \nLet $\\mathcal { N } ( s , r )$ be the set of incorrect objects to be in the triplet $( s , r , \\cdot )$ . ", + "bbox": [ + 173, + 728, + 820, + 761 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our objective function uses the ranking loss to measure the margin between the scores of true answers and those of false answers and it can be written as follows: ", + "bbox": [ + 173, + 766, + 821, + 795 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/d0cca07bb8163d14a796bc213dc59912b521bb4b485d6c47e59ae0830c053954.jpg", + "text": "$$\n\\begin{array} { r } { \\displaystyle \\underset { \\{ \\delta _ { r } , M _ { r } , : r \\in \\bar { \\mathcal { R } } \\} } { \\operatorname* { m i n } } \\frac { 1 } { N } \\sum _ { ( s , r , o ) \\in \\mathcal { T } } \\mathbb { E } _ { t ^ { \\prime } \\sim \\mathcal { N } ( s , r ) } \\left[ [ \\mu - \\mathrm { s c o r e } ( s , r , o ) + \\mathrm { s c o r e } ( s , r , t ^ { \\prime } ) ] _ { + } \\right] } \\\\ { + \\lambda \\left( \\displaystyle \\sum _ { e \\in \\mathcal { E } } \\| v _ { e } \\| _ { 2 } ^ { 2 } + \\displaystyle \\sum _ { r \\in \\bar { \\mathcal { R } } } \\big ( \\| \\delta _ { r } \\| _ { 2 } ^ { 2 } + \\| M _ { r } \\| _ { F } ^ { 2 } \\big ) \\right) , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 250, + 796, + 746, + 892 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where, $N = | \\mathcal { T } |$ , $\\mu$ is the margin parameter and $M _ { r }$ denotes the diagonal matrix with $m _ { r , j } , j =$ $1 , \\ldots , d$ on the diagonal; the function $[ \\cdot ] _ { + }$ is defined as $[ x ] _ { + } = \\operatorname* { m a x } ( 0 , x )$ . Here, we treat an inverse relation as a separate relation and denote by $\\bar { \\mathcal { R } } = \\mathcal { R } \\cup \\mathcal { R } ^ { - 1 }$ the set of all the relations including both relations in $\\mathcal { R }$ and their inverse relations; a relation $\\tilde { r }$ is the inverse relation of $r$ if $( s , \\tilde { r } , o )$ implies $( o , r , s )$ and vice versa. Moreover, $\\mathbb { E } _ { t ^ { \\prime } \\sim \\mathcal { N } ( s , r ) }$ denotes the expectation with respect to the uniform distribution over the set of incorrect objects, which we approximate with 10 random samples in the experiments. Finally, the last terms are $\\ell _ { 2 }$ regularization terms for the embedding parameters. ", + "bbox": [ + 173, + 895, + 823, + 925 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 102, + 825, + 174 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.2 COMPOSITIONAL RELATIONS ", + "text_level": 1, + "bbox": [ + 176, + 190, + 415, + 203 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Guu et al. (2015) has recently shown that training TransE with compositional relations can make it competitive to more complex models, although TransE is much simpler compared to for example, neural tensor networks (NTN, Socher et al. (2013)) and TransH Wang et al. (2014). Here, a compositional relation is a relation that is composed as a series of relations in $\\mathcal { R }$ , for example, grand father of can be composed as first applying the parent of relation and then the father of relation, which can be seen as a traversal over a path on the knowledge graph. ", + "bbox": [ + 173, + 215, + 825, + 300 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "TransGaussian model can naturally handle and propagate the uncertainty over such a chain of relations by convolving the Gaussian distributions along the path. That is, the score of an entity $o$ to be in the $\\tau$ -step relation $r _ { 1 } / r _ { 2 } / \\cdots / r _ { \\tau }$ with subject $s$ , which we denote by the triplet $( \\dot { s , } r _ { 1 } / r _ { 2 } / \\cdot \\cdot \\cdot / r _ { \\tau } , o )$ , is given as ", + "bbox": [ + 174, + 306, + 825, + 362 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/cb93d0b8c285b8098298d11c8377beb8dea13fa379d403f59d98150719afc4c2.jpg", + "text": "$$\n\\begin{array} { r } { \\mathrm { s c o r e } ( s , r _ { 1 } / r _ { 2 } / \\cdot \\cdot \\cdot / r _ { \\tau } , o ) = \\log \\phi ( \\pmb { v } _ { o } | \\pmb { \\mu } _ { \\mathrm { c o n t e x t } } , \\pmb { \\Sigma } _ { \\mathrm { c o n t e x t } } ) , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 297, + 364, + 696, + 381 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $\\begin{array} { r } { \\pmb { \\mu } _ { \\mathrm { c o n t e x t } } = \\pmb { v } _ { s } + \\sum _ { t = 1 } ^ { \\tau } \\delta _ { r _ { t } } } \\end{array}$ , $\\begin{array} { r } { \\sum _ { \\mathrm { c o n t e x t } } = \\sum _ { t = 1 } ^ { \\tau } \\sum _ { r _ { t } } } \\end{array}$ , where the covariance associated with each relation is parameterized in the same way as in the previous subsection. ", + "bbox": [ + 173, + 383, + 830, + 414 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training with compositional relations Let P = n\u0010si, ri1 /ri2 / · · · /rili , oi\u0011oN i=1 be a set of randomly sampled paths from the knowledge graph. Here relation $r _ { i _ { k } }$ in a path can be a relation in $\\mathcal { R }$ or an inverse relation in $\\mathcal { R } ^ { - 1 }$ . With the scoring function (4), the generalized training objective for compositional relations can be written identically to (3) except for replacing $\\tau$ with $\\mathcal { T } \\cup \\mathcal { P }$ and replacing $N$ with $N ^ { \\prime } = | \\mathcal { T } \\cup \\mathcal { P } |$ . ", + "bbox": [ + 174, + 430, + 825, + 511 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3 QUESTION ANSWERING ", + "text_level": 1, + "bbox": [ + 176, + 530, + 401, + 546 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a set of question-answer pairs, in which the question is phrased in natural language and the answer is an entity in the knowledge base, our goal is to train a model that learns the mapping from the question to the correct entity. Our question answering model consists of three steps, entity recognition, relation composition, and conjunction. We first identify a list of entities mentioned in the question (which is assumed to be provided by an oracle in this paper). If the question is “Who plays Forward for Borussia Dortmund?” then the list would be [Forward, Borussia Dortmund]. The next step is to predict the path of relations on the knowledgegraph starting from each entity in the list extracted in the first step. In the above example, this will be (smooth versions of) /Forward/position played by/ and /Borussia Dortmund/has player/ predicted as series of Gaussian convolutions. In general, we can have multiple relations appearing in each path. Finally, we take a product of all the Gaussian attentions and renormalize it, which is equivalent to Bayes’ rule with independent observations (paths) and a noninformative prior. ", + "bbox": [ + 174, + 560, + 825, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1 ENTITY RECOGNITION ", + "text_level": 1, + "bbox": [ + 176, + 743, + 370, + 757 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We assume that there is an oracle that provides a list containing all the entities mentioned in the question, because (1) a domain specific entity recognizer can be developed efficiently (Williams et al., 2015) and (2) generally entity recognition is a challenging task and it is beyond the scope of this paper to show whether there is any benefit in training our question answering model jointly with a entity recognizer. We assume that the number of extracted entities can be different for each question. ", + "bbox": [ + 174, + 770, + 825, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2 RELATION COMPOSITION ", + "text_level": 1, + "bbox": [ + 176, + 869, + 388, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We train a long short-term memory (LSTM, Hochreiter & Schmidhuber, 1997) network that emits an output $\\boldsymbol { h } _ { t }$ for each token in the input sequence. Then we compute the attention over the hidden ", + "bbox": [ + 174, + 895, + 823, + 924 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c8be4c487573afc71d590a3b723235da8f6bd144ebef356a786893ec5f627b32.jpg", + "image_caption": [ + "Figure 2: The input to the system is a question in natural language. Two entities Forward and Borussia Dortmund are identified in the question and associated with point mass distributions centered at the corresponding entity vectors. An LSTM encodes the input into a sequence of output vectors of the same length. Then we take average of the output vectors weighted by attention $\\mathit { p } _ { t , e }$ for each recognized entity $e$ to predict the weight $\\alpha _ { r , e }$ for relation $r$ associated with entity $e$ . We form a Gaussian attention over the entities for each entity $e$ by convolving the corresponding point mass with the (pre-trained) Gaussian embeddings of the relations weighted by $\\alpha _ { r , e }$ according to Eq. (6). The final prediction is produced by taking the product and normalizing the Gaussian attentions. " + ], + "image_footnote": [], + "bbox": [ + 174, + 103, + 834, + 376 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "states for each recognized entity $e$ as ", + "bbox": [ + 176, + 531, + 416, + 545 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/6a31c5c001b680422b7d6aafeee5203c2e1e12300f556bf38b98a9f0280e2f71.jpg", + "text": "$$\np _ { t , e } = \\mathrm { s o f t m a x } \\left( f ( v _ { e } , h _ { t } ) \\right) \\quad ( t = 1 , . . . , T ) ,\n$$", + "text_format": "latex", + "bbox": [ + 348, + 550, + 647, + 568 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where ${ \\pmb v } _ { e }$ is the vector associated with the entity $e$ . We use a two-layer perceptron for $f$ in our experiments, which can be written as follows: ", + "bbox": [ + 173, + 571, + 825, + 599 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/b54c9eabaf2cfb70e6f9942a009c5b30d6b3c5e53c41a45f71514307ec4003ec.jpg", + "text": "$$\nf ( \\pmb { v } _ { e } , \\pmb { h } _ { t } ) = \\pmb { u } _ { f } ^ { \\top } \\mathrm { R e L U } \\left( \\pmb { W } _ { f , v } \\pmb { v } _ { e } + \\pmb { W } _ { f , h } \\pmb { h } _ { t } + \\pmb { b } _ { 1 } \\right) + b _ { 2 } ,\n$$", + "text_format": "latex", + "bbox": [ + 312, + 606, + 684, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf { \\widetilde { \\Gamma } } _ { f , v } \\in \\mathbb { R } ^ { L \\times d } , W _ { f , h } \\in \\mathbb { R } ^ { L \\times H } , b _ { 1 } \\in \\mathbb { R } ^ { L } , { \\mathbf { u } } _ { f } \\in \\mathbb { R } ^ { L } , b _ { 2 } \\in \\mathbb { R } \\mathrm { a r e } \\mathrm { p a r }$ ameters. Here ${ \\mathrm { R e L U } } ( x ) =$ $\\operatorname* { m a x } ( 0 , x )$ is the rectified linear unit. Finally, softmax denotes softmax over the $T$ tokens. ", + "bbox": [ + 173, + 631, + 821, + 660 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, we use the weights $\\mathit { p } _ { t , e }$ to compute the weighted sum over the hidden states $\\boldsymbol { h } _ { t }$ as ", + "bbox": [ + 173, + 666, + 748, + 681 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/2b53a112ee0c39aded391dee712421d6078d99ad25424f6d26c2802163f13eaf.jpg", + "text": "$$\no _ { e } = \\sum _ { t = 1 } ^ { T } p _ { t , e } h _ { t } .\n$$", + "text_format": "latex", + "bbox": [ + 431, + 685, + 566, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then we compute the weights $\\alpha _ { r , e }$ over all the relations as $\\alpha _ { r , e } = \\mathrm { R e L U } \\left( \\pmb { w } _ { r } ^ { \\top } \\pmb { o } _ { e } \\right) \\quad \\left( \\forall r \\in \\mathcal { R } \\cup \\right.$ $\\mathcal { R } ^ { - 1 }$ ). Here the rectified linear unit is used to ensure the positivity of the weights. Note however that the weights should not be normalized, because we may want to use the same relation more than once in the same path. Making the weights positive also has the effect of making the attention sparse and interpretable because there is no cancellation. ", + "bbox": [ + 173, + 727, + 825, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each extracted entity $e$ , we view the extracted entity and the answer of the question to be the subject and the object in some triplet $( e , p , o )$ , respectively, where the path $p$ is inferred from the question as the weights $\\alpha _ { r , e }$ as we described above. Accordingly, the score for each candidate answer $o$ can be expressed using (1) as: ", + "bbox": [ + 173, + 806, + 825, + 864 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/2bda7cc08ca20184c9dd2f7776ba0063ba8e71d48f6c8123f749f089080f9874.jpg", + "text": "$$\n\\mathrm { s c o r e } _ { e } ( \\pmb { v } _ { o } ) = \\log \\phi ( \\pmb { v } _ { o } | \\pmb { \\mu } _ { e , \\alpha , \\mathrm { K B } } , \\pmb { \\Sigma } _ { e , \\alpha , \\mathrm { K B } } )\n$$", + "text_format": "latex", + "bbox": [ + 361, + 868, + 635, + 887 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with $\\begin{array} { r } { \\pmb { \\mu } _ { e , \\alpha , \\mathrm { K B } } = \\pmb { v } _ { e } + \\sum _ { r \\in \\bar { \\mathcal { R } } } \\alpha _ { r , e } \\delta _ { r } , \\sum _ { e , \\alpha , \\mathrm { K B } } = \\sum _ { r \\in \\bar { \\mathcal { R } } } \\alpha _ { r , e } ^ { 2 } \\pmb { \\Sigma } _ { r } } \\end{array}$ , where ${ \\pmb v } _ { e }$ is the vector associated with entity $e$ and $\\bar { \\mathcal { R } } = \\mathcal { R } \\cup \\mathcal { R } ^ { - 1 }$ denotes the set of relations including the inverse relations. ", + "bbox": [ + 178, + 891, + 825, + 924 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3 CONJUNCTION ", + "text_level": 1, + "bbox": [ + 174, + 103, + 318, + 117 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Let $\\mathcal { E } ( q )$ be the set of entities recognized in the question $q$ . The final step of our model is to take the conjunction of the Gaussian attentions derived in the previous step. This step is simply carried out by multiplying the Gaussian attentions as follows: ", + "bbox": [ + 173, + 128, + 825, + 171 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/7a525619e51c23780d45b9a7021f18a63cee7243fd7e4bee1093ec968f13bce2.jpg", + "text": "$$\n\\begin{array} { r l } & { \\mathrm { s c o r e } ( \\pmb { v } _ { o } | \\mathcal { E } ( q ) , \\Theta ) = \\underset { e \\in \\mathcal { E } ( q ) } { \\log \\prod } \\phi ( \\pmb { v } _ { o } | \\pmb { \\mu } _ { e , \\alpha , \\mathrm { K B } } , \\pmb { \\Sigma } _ { e , \\alpha , \\mathrm { K B } } ) } \\\\ & { \\qquad = - \\cfrac { 1 } { 2 } \\displaystyle \\sum _ { e \\in \\mathcal { E } ( q ) } \\left( \\pmb { v } _ { o } - \\pmb { \\mu } _ { e , \\alpha , \\mathrm { K B } } \\right) ^ { \\top } \\pmb { \\Sigma } _ { e , \\alpha , \\mathrm { K B } } ^ { - 1 } ( \\pmb { v } _ { o } - \\pmb { \\mu } _ { e , \\alpha , \\mathrm { K B } } ) + \\mathrm { c o n s t . } , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 223, + 172, + 772, + 251 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "which is again a (logarithm of) Gaussian scoring function, where $\\mu _ { e , \\alpha , \\mathrm { K B } }$ and $\\Sigma _ { e , \\alpha , \\mathrm { K B } }$ are the mean and the covariance of the Gaussian attention given in (6). Here $\\Theta$ denotes all the parameters of the question-answering model. ", + "bbox": [ + 176, + 251, + 825, + 294 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4 TRAINING THE QUESTION ANSWERING MODEL ", + "text_level": 1, + "bbox": [ + 174, + 309, + 537, + 324 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Suppose we have a knowledge base $( \\mathcal { E } , \\mathcal { R } , \\mathcal { T } )$ and a trained TransGaussian model $\\big ( \\{ v _ { e } \\} _ { e \\in \\mathcal { E } } , \\{ ( \\delta _ { r } , \\Sigma _ { r } ) \\} _ { r \\in \\bar { \\mathcal { R } } } \\big )$ , where $\\bar { \\mathcal { R } }$ is the set of all relations including the inverse relations. During training time, we assume the training set is a supervised question-answer pairs $\\{ ( q _ { i } , \\mathcal { E } ( q _ { i } ) , a _ { i } \\bar { ) } : i = 1 , 2 , . . . , m \\}$ . Here, $q _ { i }$ is a question formulated in natural language, $\\bar { \\mathcal { E } } ( q _ { i } ) \\subset \\mathcal { E }$ is a set of knowledge base entities that appears in the question, and $a _ { i } ~ \\in { \\mathcal { E } }$ is the answer to the question. For example, on a knowledge base of soccer players, a valid training sample could be ", + "bbox": [ + 174, + 334, + 825, + 421 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(“Who plays forward for Borussia Dortmund?”,[Forward, Borussia Dortmund], Marco Reus). ", + "bbox": [ + 173, + 426, + 834, + 443 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that the answer to a question is not necessarily unique and we allow $a _ { i }$ to be any of the true answers in the knowledge base. During test time, our model is shown $\\left( q _ { i } , \\mathcal { E } ( q _ { i } ) \\right)$ and the task is to find $a _ { i }$ . We denote the set of answers to $q _ { i }$ by $A ( q _ { i } )$ . ", + "bbox": [ + 174, + 448, + 828, + 492 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To train our question-answering model, we minimize the objective function ", + "bbox": [ + 176, + 497, + 669, + 512 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/da79e56167ea45f43a99cc298820ad1427c0d4cc335951436f969b82dfa3a070.jpg", + "text": "$$\n\\frac { 1 } { n } \\sum _ { i = 1 } ^ { m } \\biggl ( \\underset { t ^ { \\prime } \\sim \\mathcal { N } ( q _ { i } ) } { \\mathbb { E } } \\left[ [ \\mu - \\mathrm { s c o r e } ( v _ { a _ { i } } | \\mathcal { E } ( q _ { i } ) , \\Theta ) + \\mathrm { s c o r e } ( v _ { t ^ { \\prime } } | \\mathcal { E } ( q _ { i } ) , \\Theta ) ] _ { + } \\right] + \\nu \\sum _ { e \\in \\mathcal { E } ( q _ { i } ) } \\sum _ { r \\in \\mathcal { R } } | \\alpha _ { r , e } | \\biggr ) + \\lambda \\| \\Theta \\| _ { 2 } ^ { 2 }\n$$", + "text_format": "latex", + "bbox": [ + 181, + 515, + 838, + 558 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbb { E } _ { t ^ { \\prime } \\sim \\mathcal { N } ( q _ { i } ) }$ is expectation with respect to a uniform distribution over of all incorrect answers to $q _ { i }$ , which we approximate with 10 random samples. We assume that the number of relations implied in a question is small compared to the total number of relations in the knowledge base. Hence the coefficients $\\alpha _ { r , e }$ computed for each question $q _ { i }$ are regularized by their $\\ell _ { 1 }$ norms. ", + "bbox": [ + 174, + 559, + 826, + 616 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4 EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 635, + 326, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As a demonstration of the proposed framework, we perform question and answering on a dataset of soccer players. In this work, we consider two types of questions. A path query is a question that contains only one named entity from the knowledge base and its answer can be found from the knowledge graph by walking down a path consisting of a few relations. A conjunctive query is a question that contains more than one entities and the answer is given as the conjunction of all path queries starting from each entity. Furthermore, we experimented on a knowledge base completion task with TransGaussian embeddings to test its capability of generalization to unseen fact. Since knowledge base completion is not the main focus of this work, we include the results in the Appendix. ", + "bbox": [ + 174, + 664, + 825, + 790 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1 WORLDCUP2014 DATASET ", + "text_level": 1, + "bbox": [ + 176, + 806, + 401, + 820 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We build a knowledge base of football players that participated in FIFA World Cup 2014 1. The original dataset consists of players’ information such as nationality, positions on the field and ages etc. We picked a few attributes and constructed 1127 entities and 6 atomic relations. The entities include 736 players, 297 professional soccer clubs, 51 countries, 39 numbers and 4 positions. And the six atomic relations are plays in club: PLAYER $ \\mathrm { C L U B }$ , is aged: PLAYER NUMBER, plays for country: PLAYER COUNTRY, plays position: PLAYER POSITION, wears number 2: PLAYER NUMBER, is in country: CLUB COUNTRY, ", + "bbox": [ + 174, + 832, + 823, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "", + "bbox": [ + 181, + 101, + 519, + 143 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 537, + 102, + 848, + 143 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where PLAYER, CLUB, NUMBER, etc, denote the type of entities that can appear as the left or right argument for each relation. Some relations share the same type as the right argument, e.g., plays for country and is in country. ", + "bbox": [ + 176, + 143, + 826, + 185 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Given the entities and relations, we transformed the dataset into a set of 3977 triplets. A list of sample triplets can be found in the Appendix. Based on these triplets, we created two sets of question answering tasks which we call path query and conjunctive query respectively. The answer of every question is always an entity in the knowledge base and a question can involve one or two triplets. The questions are generated as follows. ", + "bbox": [ + 174, + 193, + 825, + 262 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Path queries. Among the paths on the knowledge graph, there are some natural composition of relations, e.g., plays in country (PLAYER COUNTRY) can be decomposed as the composition of plays in club (PLAYE $\\mathbf { R } \\to \\mathbf { C L } $ UB) and is in country $( \\mathbf { C L U B } \\to \\mathbf { C O U N T R Y } )$ . In addition to the atomic relations, we manually picked a few meaningful compositions of relations and formed query templates, which takes the form “find $e \\in { \\mathcal { E } }$ , such that $( s , p , e )$ is true”, where $s$ is the subject and $p$ can be an atomic relation or a path of relations. To formulate a set of path-based question-answer pairs, we manually created one or more question templates for every query template (see Table 5) Then, for a particular instantiation of a query template with subject and object entities, we randomly select a question template to generate a question given the subject; the object entity becomes the answer of the question. See Table 6 for the list of composed relations, sample questions, and answers. Note that all atomic relations in this dataset are many-to-one while these composed relations can be one-to-many or many-to-many as well. ", + "bbox": [ + 173, + 279, + 825, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Conjunctive queries. To generate question-and-answer pairs of conjunctive queries, we first picked three pairs of relations and used them to create query templates of the form “Find $e \\in { \\mathcal { E } }$ , such that both $( s _ { 1 } , r _ { 1 } , e )$ and $( s _ { 2 } , r _ { 2 } , e )$ are true.” (see Table 5). For a pair of relations $r _ { 1 }$ and $r _ { 2 }$ , we enumerated all pairs of entities $s _ { 1 } , s _ { 2 }$ that can be their subjects and formulated the corresponding query in natural language using question templates as in the same way as path queries. See Table 7 for a list of sample questions and answers. ", + "bbox": [ + 174, + 460, + 825, + 544 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As a result, we created 8003 question-and-answer pairs of path queries and 2208 pairs of conjunctive queries which are partitioned into train / validation $/$ test subsets. We refer to Table 1 for more statistics about the dataset. Templates for generating the questions are list in Table 5. ", + "bbox": [ + 174, + 551, + 825, + 593 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2 EXPERIMENTAL SETUP ", + "text_level": 1, + "bbox": [ + 176, + 611, + 372, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To perform question and answering under our proposed framework, we first train the TransGaussian model on WorldCup2014 dataset. In addition to the atomic triplets, we randomly sampled 50000 paths with length 1 or 2 from the knowledge graph and trained a TransGaussian model compositionally as described in Set 2.2. An inverse relation is treated as a separate relation. Following the naming convention from Guu et al. (2015), we denote this trained embedding by TransGaussian (COMP). We found that the learned embedding possess some interesting properties. Some dimensions of the embedding space dedicate to represent a particular relation. Players are clustered by their attributes when entities’ embeddings are projected to the corresponding lower dimensional subspaces. We elaborate and illustrate such properties in the Appendix. ", + "bbox": [ + 174, + 636, + 825, + 761 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baseline methods We also trained a TransGaussian model only on the atomic triplets and denote such a model by TransGaussian (SINGLE). Since no inverse relation was involved when TransGaussian (SINGLE) was trained, to use this embedding in question answering tasks, we represent the inverse relations as follows: for each relation $r$ with mean $\\delta _ { r }$ and variance $\\Sigma _ { r }$ , we model its inverse $r ^ { - 1 }$ as a Gaussian attention with mean $- \\delta _ { r }$ and variance equal to $\\Sigma _ { r }$ . ", + "bbox": [ + 174, + 776, + 823, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also trained TransE models on WorldCup2014 dataset by using the code released by the authors of Guu et al. (2015). Likewise, we use TransE (SINGLE) to denote the model trained with atomic triplets only and use TransE (COMP) to denote the model trained with the union of triplets and paths. Note that TransE can be considered as a special case of TransGaussian where the variance matrix is the identity and hence, the scoring formula Eq. (7) is applicable to TransE as well. ", + "bbox": [ + 174, + 853, + 823, + 924 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training configurations For all models, dimension of entity embeddings was set to 30. The hidden size of LSTM was set to 80. Word embeddings were trained jointly with the question answering model and dimension of word embedding was set to 40. We employed Adam (Kingma & Ba, 2014) as the optimizer. All parameters were tuned on the validation set. Under the same setting, we experimented with two cases: first, we trained models for path queries and conjunctive queries separately; Furthermore, we trained a single model that addresses both types queries. We present the results of the latter case in the next subsection while the results of the former are included in the Appendix. ", + "bbox": [ + 174, + 103, + 825, + 200 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Evaluation metrics During test time, our model receives a question in natural language and a list of knowledge base entities contained in the question. Then it predicts the mean and variance of a Gaussian attention formulated in Eq. (7) which is expected to capture the distribution of all positive answers. We rank all entities in the knowledge base by their scores under this Gaussian attention. Next, for each entity which is a correct answer, we check its rank relative to all incorrect answers and call this rank the filtered rank. For example, if a correct entity is ranked above all negative answers except for one, it has filtered rank two. We compute this rank for all true answers and report mean filtered rank and $H @ l$ which is the percentage of true answers that have filtered rank 1. ", + "bbox": [ + 174, + 215, + 825, + 328 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3 EXPERIMENTAL RESULTS ", + "text_level": 1, + "bbox": [ + 176, + 344, + 390, + 358 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present the results of joint learning in Table 2. These results show that TransGaussian works better than TransE in general. In fact, TransGaussian (COMP) achieved the best performance in almost all aspects. Most notably, it achieved the highest $\\mathrm { H @ 1 }$ rates on challenging questions such as “where is the club that edin dzeko plays for?” (#11, composition of two relations) and “who are the defenders on german national team?” (#14, conjunction of two queries). ", + "bbox": [ + 174, + 369, + 825, + 440 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The same table shows that TransGaussian benefits remarkably from compositional training. For example, compositional training improved TransGaussian’s $\\mathrm { H @ 1 }$ rate by near $60 \\%$ in queries on players from a given countries (#8) and queries on players who play a particular position (#9). It also boosted TransGaussian’s performance on all conjunctive quries (#13–#15) significantly. ", + "bbox": [ + 174, + 446, + 825, + 502 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To understand TransGaussian (COMP)’s weak performance on answering queries on the professional football club located in a given country (#10) and queries on professional football club that has players from a particular country (#12), we tested its capability of modeling the composed relation by feeding the correct relations and subjects during test time. It turns out that these two relations were not modeled well by TransGaussian (COMP) embedding, which limits its performance in question answering. (See Table 8 in the Appendix for quantitative evaluations.) The same limit was found in the other three embeddings as well. ", + "bbox": [ + 174, + 510, + 825, + 608 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Note that all the models compared in Table 2 uses the proposed Gaussian attention model because TransE is the special case of TransGaussian where the variance is fixed to one. Thus the main differences are whether the variance is learned and whether the embedding was trained compositionally. Finally, we refer to Table 9 and 10 in the Appendix for experimental results of models trained on path and conjunctive queries separately. ", + "bbox": [ + 174, + 614, + 825, + 685 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/aad02463c0fedf6a70824602adf903d1fff0827b0c92885dcdc8d3417dc51591.jpg", + "table_caption": [ + "Table 1: Some statistics of the WorldCup2014 dataset. " + ], + "table_footnote": [], + "table_body": "
# entity
#atomic relations# atomic triplets
# path query Q&A（train/validation/test）# conjunctive query Q&A（train /validation /test）
1127639775620/804/15791564/224/420
", + "bbox": [ + 174, + 722, + 874, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5 RELATED WORK ", + "text_level": 1, + "bbox": [ + 176, + 795, + 341, + 810 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The work of Vilnis & McCallum (2014) is similar to our Gaussian attention model. They discuss many advantages of the Gaussian embedding; for example, it is arguably a better way of handling asymmetric relations and entailment. However the work was presented in the word2vec (Mikolov et al., 2013)-style word embedding setting and the Gaussian embedding was used to capture the diversity in the meaning of a word. Our Gaussian attention model extends their work to a more general setting in which any memory item can be addressed through a concept represented as a Gaussian distribution over the memory items. ", + "bbox": [ + 173, + 825, + 825, + 924 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7b655a2b41aad14dfeb2d35e01d31e0083bc112661b419140489d25d63616d5e.jpg", + "table_caption": [ + "Table 2: Results of joint learning with path queries and conjunction queries on WorldCup2014. " + ], + "table_footnote": [], + "table_body": "
TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#Sample questionH@1(%）FilteredMean RankH@1(%）FilteredMean RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered Rank
1which club does alan pulido play for?88.591.1891.951.1196.641.0498.661.01
2what position does gonzalo higuain play?100.001.0098.111.0398.741.01100.001.00
3how old is samuel etoo?67.111.4490.791.1394.741.0897.371.04
4what is the jersey number of mario balotelli?45.001.8983.571.2297.141.0399.291.01
5which country is thomas mueller from ?94.401.0694.401.0696.801.0498.401.02
6which country is the soccer team fc porto based in ?98.481.0298.481.0293.941.0695.451.05
7who plays professionally at liverpool fc?95.121.1090.241.2098.371.0496.751.04
8which player is from iran?89.861.5176.812.0738.652.9699.521.00
9name a player who plays goalkeeper?98.961.0169.791.8242.715.52100.001.00
10which soccer club is based in mexico?22.0313.9430.518.846.7810.6616.9521.14
11where is the club that edin dzeko plays for ？52.633.8857.242.1047.372.2778.291.41
12name a soccer club that has a player from australia ?30.4312.0833.7011.4713.0411.6419.5717.57
Overall (Path Query)74.163.1177.392.5669.543.0285.943.52
13who plays forward for fc barcelona?97.551.0676.071.6693.251.2498.771.02
14who are the defenders on german national team?95.931.0669.922.3365.042.04100.001.00
15which player in ssc napoli is from argentina?88.811.1776.121.7688.811.3597.761.03
Overall(Conj. Query)94.291.0974.291.8983.571.5198.811.02
", + "bbox": [ + 173, + 126, + 834, + 333 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Bordes et al. (2014; 2015) proposed a question-answering model that embeds both questions and their answers to a common continuous vector space. Their method in Bordes et al. (2015) can combine multiple knowledge bases and even generalize to a knowledge base that was not used during training. However their method is limited to the simple question answering setting in which the answer of each question associated with a triplet in the knowledge base. In contrast, our method can handle both composition of relations and conjunction of conditions, which are both naturally enabled by the proposed Gaussian attention model. ", + "bbox": [ + 174, + 367, + 825, + 464 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Neelakantan et al. (2015a) proposed a method that combines relations to deal with compositional relations for knowledge base completion. Their key technical contribution is to use recurrent neural networks (RNNs) to encode a chain of relations. When we restrict ourselves to path queries, question answering can be seen as a sequence transduction task (Graves, 2012; Sutskever et al., 2014) in which the input is text and the output is a series of relations. If we use RNNs as a decoder, our model would be able to handle non-commutative composition of relations, which the current weighted convolution cannot handle well. Another interesting connection to our work is that they take the maximum of the inner-product scores (see also Weston et al., 2013; Neelakantan et al., 2015b), which are computed along multiple paths connecting a pair of entities. Representing a set as a collection of vectors and taking the maximum over the inner-product scores is a natural way to represent a set of memory items. The Gaussian attention model we propose in this paper, however, has the advantage of differentiability and composability. ", + "bbox": [ + 174, + 472, + 825, + 638 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6 CONCLUSION ", + "text_level": 1, + "bbox": [ + 176, + 666, + 318, + 681 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we have proposed the Gaussian attention model which can be used in a variety of contexts where we can assume that the distance between the memory items in the latent space is compatible with some notion of semantics. We have shown that the proposed Gaussian scoring function can be used for knowledge base embedding achieving competitive accuracy. We have also shown that our embedding model can naturally propagate uncertainty when we compose relations together. Our embedding model also benefits from compositional training proposed by Guu et al. (2015). Furthermore, we have demonstrated the power of the Gaussian attention model in a challenging question answering problem which involves both composition of relations and conjunction of queries. Future work includes experiments on natural question answering datasets and end-to-end training including the entity extractor. ", + "bbox": [ + 174, + 702, + 825, + 842 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "ACKNOWLEDGMENTS ", + "text_level": 1, + "bbox": [ + 176, + 867, + 326, + 880 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The authors would like to thank Daniel Tarlow, Nate Kushman, and Kevin Gimpel for valuable discussions. ", + "bbox": [ + 174, + 895, + 821, + 922 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "REFERENCES ", + "text_level": 1, + "bbox": [ + 176, + 102, + 287, + 118 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv:1409.0473, 2014. 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", + "bbox": [ + 173, + 306, + 825, + 363 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "A WORDCUP2014 DATASET ", + "text_level": 1, + "bbox": [ + 176, + 102, + 423, + 117 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/c76b54d069c446a577d193f3e4e7991307a9815e447eeaf69529984549fe539d.jpg", + "table_caption": [ + "Table 3: Sample atomic triplets. " + ], + "table_footnote": [], + "table_body": "
SubjectRelationObject
david_villaplays-for_countryspain
lionel_messiplays_in-clubfc_barcelona
antoine-griezmannplays-positionforward
cristiano_ronaldowears_number7
fulham_fcis_in_countryengland
lukas_podolskiis_aged29
", + "bbox": [ + 339, + 171, + 655, + 247 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/2745f1e997fc7c77d598f00975f60d1aef2225ce169b2b4d4728c20044684904.jpg", + "table_caption": [ + "Table 4: Statistics of the WorldCup2014 dataset. " + ], + "table_footnote": [], + "table_body": "
#entity# atomic relations# atomic triplets112763977
#relations (atomic and compositional) in path queries# question and answer pairs in path queries(train/validation/ test）125620/804/1579
# types of questions in conjunctive queries# question and answer pairs in conjunctive queries(train/validation/test )31564/224/420
size of vocabulary1781
", + "bbox": [ + 263, + 334, + 732, + 420 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/5c8936e2f39543c1538d4f7c684c5e78d08c0646e6073693b5ca4bc83415e80b.jpg", + "table_caption": [ + "Table 5: Templates of questions. In the table, (player), (club), (position) are placeholders of named entities with associated type. (country 1) is a placeholder for a country name while (country 2) is a placeholder for the adjectival form of a country. " + ], + "table_footnote": [], + "table_body": "
#Query templateQuestion template
1Finde ∈ε:((player),plays_in_club,e)is truewhich club does (player) play for ?which professional football team does (player) play for ?which football club does (player) play for ?
2Finde∈ε:(player),plays-position,e)is truewhat position does (player) play ?
3Find e ∈ε:(player),is-aged,e) is truehow old is (player) ?what is the age of (player) ?
4Finde∈ε:(player),wears_number,e) is truewhat is the jersey number of (player) ?what number does (player) wear ?
5Finde ∈ε:(player),plays_for_country,e) is truewhat is the nationality of (player) ?which national team does (player) play for ?which country is (player) from ?
6Finde∈ε:(club),is-in_country,e)is truewhich country is the soccer team (club) based in ?
7Finde ∈ε: (club),plays_in_club-1,e)is truename a player from (club) ?who plays at the soccer club (club) ?who is from the professional football team (club) ?who plays professionally at (club) ?
8Finde ∈ε:(country-1),plays_for-country-1,e)is truewhich player is from (country_1) ?name a player from (country-1) ?who is from (country-1) ?who plays for the (country_1) national football team ?
9Finde∈ε:(position),playsposition-,e)is truename a player who plays (position) ?who plays (position) ?
10Finde ∈ε:(cotry-1),sicountry-1,e)is truewhich soccer club is based in (country_1) ?name a soccer club in (country_1) ?
11Finde∈ε:(player),plays_in_club /is_in_country,e)is truewhich country does (player) play professionally in ?where is the football club that (player) plays for ?
12Finde ∈ε:(country-1),plays-for-country-1/plays_in_club,e)is truewhich professional football team do players from (country_1) play for ？name a soccer club that has a player from (country_1) ?which professional football team has a player from (country_1) ?
13Find e∈ ε:(position),plays-position-1,e) is true and((club),plays-in_club-1,e) is truewho plays (position) for (club)?who are the (position) at (club) ?name a (position) that plays for (club) ?
14Find e∈ε: (position),plays-position-1,e) is true and(country-l),plays-for-country-1,e)is truewho plays (position) for (country_1) ?who are the (position) on (country_1) national team ?name a (position) from (country-1) ?which (country_2) footballer plays (position) ?name a (country-2) (position) ?
15Find e∈ε:(club)， plays_in_club-1,e) is true and(country_l),plays_for_country-1,e)is truewho are the (country_2) playersat (club)？which (country_2) footballer plays for (club) ?name a (country_2) player at (club) ?which player in (club) is from (country-1) ?
", + "bbox": [ + 173, + 505, + 864, + 909 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/1e08d92fcdcdcb4612cfc8a344544f32e1c03b71996f84931a70e6d731e7a783.jpg", + "table_caption": [ + "Table 6: (Composed) relations and sample questions in path queries. " + ], + "table_footnote": [], + "table_body": "
#RelationTypeSample questionSample answer
1plays_in_clubmany-to-onewhich club doesalan pulido play for ?which professional footbal team does klaas jan huntelar play for ?tigres_uanlfc_schalke_04
2plays-positionmany-to-onewhat position does gonzalo higuain play ?ssc_napoli
3is_agedmany-to-onehow old is samuel etoo ?what is the age of luis suarez ?3
4wears-numbermany-to-onewhat is the jersey number of mario balotelli ?what number does shinji okazaki wear ?：
5plays_for_countrymany-to-onewhich country is thomas mueller from ?what is the nationality of helder postiga ?germanyportugal
6is.in_countrymany-to-onewhich country is the soccer team fc porto based in ?portugal
7plays_in_club-1one-to-manywho playsprofessionally at liverpool fc ?name a player from as roma ?steven_gerrardmiralem_pjanic
8plays-for_country-1one-to-manywhich player is from iran ？name a player from italy ?masoud_shojaeidaniele_de_rossi
9plays-position-1one-to-manyname a player who plays goalkeeper ?who plays forward ?gianluiqi-buffonraul_jimenez
10is_in-country-1one-to-manywhich soccer club is based in mexico ?name a soccer club in australia ?cruz_azul.fcmelbourne_victory_fc
11plays_in_club /is_in_countrymany-to-onewhere is the club that edin dzeko plays for ?which country does sime vrsaljko play professionally in ?englanditaly
12plays-for_country-1/plays_in_clubmany-to-manyname a soccer club that has a player from australia?name a soccer club that has a player from spain ?crystal_palace_fcfc_barcelona
", + "bbox": [ + 173, + 127, + 882, + 339 + ], + "page_idx": 12 + }, + { + "type": "table", + "img_path": "images/612204b4a493e4e6ad7548f7a46ce07e9418c499cd0449151d472e0148446f5f.jpg", + "table_caption": [ + "Table 7: Conjunctive queries and sample questions. " + ], + "table_footnote": [], + "table_body": "
#RelationsSample questionsEntities in questionsSampleanswer
13plays_position-1 and plays_in_club-1who plays forward for fc barcelona ? who are the midfielders at fc bayern muenchen ?forward,fc_barcelona midfielder,fc_bayern_muenchenlionel_messi toni_kroos
14plays-position -1 andwho are the defenders on german national team ? which mexican footballer plays forward ?defender,germany defender,mexicoper_mertesacker raul-jimenez
15plays_in_club-1 and plays_for_country -1which player in paris saint-germain fc is from argentina ? who are the korean players at beijing guoan ?paris_saint-germain_fc,argentina beijing-guoan,koreaezequiel_lavezzi ha-daesung
", + "bbox": [ + 174, + 378, + 936, + 472 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "B TRANSGAUSSIAN EMBEDDING OF WORLDCUP2014 ", + "text_level": 1, + "bbox": [ + 176, + 496, + 640, + 512 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "We trained our TransGaussian model on triplets and paths from WorldCup2014 dataset and illustrated the embeddings in Fig 3 and 4. Recall that we modeled every relation as a Gaussian with diagonal covariance matrix. Fig 3 shows the learned variance parameters of different relations. Each row corresponds to the variances of one relation. Columns are permuted to reveal the block structure. From this figure, we can see that every relation has a small variance in two or more dimensions. This implies that the coordinates of the embedding space are partitioned into semantically coherent clusters each of which represent a particular attribute of a player (or a football club). To verify this further, we picked the two coordinates in which a relation (e.g. plays position) has the least variance and projected the embedding of all valid subjects and objects (e.g. players and positions) of the relation to this 2 dimensional subspace. See Fig. 4. The relation between the subjects and the objects are simply translation in the projection when the corresponding subspace is two dimensional (e.g., plays position relation in Fig. 4 (a)). The same is true for other relations that requires larger dimension but it is more challenging to visualize in two dimensions. For relations that have a large number of unique objects, we only plotted for the eight objects with the most subjects for clarity of illustration. ", + "bbox": [ + 173, + 529, + 825, + 736 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Furthermore, in order to elucidate whether we are limited by the capacity of the TransGaussian embedding or the ability to decode question expressed in natural language, we evaluated the test question-answer pairs using the TransGaussian embedding composed according to the ground-truth relations and entities. The results were evaluated with the same metrics as in Sec. 4.3. This estimation is conducted for TransE embeddings as well. See Table 8 for the results. Compared to Table 2, the accuracy of TransGaussian (COMP) is higher on the atomic relations and path queries but lower on conjunctive queries. This is natural because when the query is simple there is not much room for the question-answering network to improve upon just combining the relations according to the ground truth relations, whereas when the query is complex the network could combine the embedding in a more creative way to overcome its limitation. In fact, the two queries (#10 and #12) that TransGaussian (COMP) did not perform well in Table 2 pertain to a single relation is in country−1 (#10) and a composition of two relations plays for country $^ - 1 \\ /$ plays in club (#12). The performance of the two queries were low even when the ground truth ", + "bbox": [ + 174, + 743, + 825, + 924 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/dcac266cd0111b767c6f604dadfa93e9478ad13210e7862e4fc0a7fbd0595157.jpg", + "image_caption": [ + "Figure 3: Variance of each relation. Each row shows the diagonal values in the variance matrix associated with a relation. Columns are permuted to reveal the block structure. " + ], + "image_footnote": [], + "bbox": [ + 246, + 107, + 764, + 246 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Table 8: Evaluation of embeddings. We evaluate the embeddings by feeding the correct entities and relations from a path or conjunctive query to an embedding model and using its scoring function to retrieve the answers from the embedded knowledge base. ", + "bbox": [ + 176, + 314, + 825, + 357 + ], + "page_idx": 13 + }, + { + "type": "table", + "img_path": "images/f2970bb498a60bf534378d87a96f1fde36b1c3928165c2aa77b7ca5bb4d95eef.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#RelationH@1(%)Mean Filtered RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered Rank
1plays.in.club75.541.3893.481.0999.861.0098.511.02
2plays-position96.331.0494.021.0998.371.02100.001.00
3is_aged55.031.6991.441.1296.881.03100.001.00
4wears_number38.862.0978.671.3295.921.04100.001.00
5plays_for_country71.601.3994.841.1099.321.01100.001.00
6is_in_country98.321.0399.661.0099.331.01100.001.00
7plays_in_club-187.501.4683.421.4594.701.0797.421.03
882.471.6868.213.3725.275.6698.781.02
9plays-position-1100.001.0075.541.6013.5924.3598.781.02
10is_in-country-123.1126.9223.4823.278.32130.5919.4183.61
11plays_in_club/is_in-country20.247.0558.291.9846.882.9980.161.38
12plays-for_country -1/plays-in_club25.3222.2727.7310.0419.0435.5920.1533.01
Overall(Path relations) plays-position-164.645.0975.023.5967.2214.8786.738.79
13and plays-in_club-1 plays-position91.851.2069.971.8277.451.8395.381.06
14and plays_in_club =T91.711.2366.712.8551.494.8897.831.05
15and is_in_country -188.591.2073.37 70.021.80 2.1683.421.3494.701.08
Overall (Conj.relations)90.721.2170.792.6895.971.06
", + "bbox": [ + 173, + 366, + 861, + 657 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "relations were given, which indicates that the TransGaussian embedding rather than the questionanswering network is the limiting factor. ", + "bbox": [ + 173, + 685, + 823, + 713 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "C KNOWLEDGE BASE COMPLETION ", + "text_level": 1, + "bbox": [ + 176, + 737, + 482, + 752 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Knowledge base completion has been a common task for testing knowledge base models on their ability of generalizing to unseen facts. Here, we apply our TransGaussian model to a knowledge completion task and show that it has competitive performance. ", + "bbox": [ + 174, + 770, + 825, + 811 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "We tested on the subset of WordNet released by Guu et al. (2015). The atomic triplets in this dataset was originally created by Socher et al. (2013) and Guu et al. (2015) added path queries that were randomly sampled from the knowledge graph. We build our TransGaussian model by training on these triplets and paths and tested our model on the same link prediction task as done by Socher et al. (2013); Guu et al. (2015). ", + "bbox": [ + 174, + 818, + 825, + 888 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "As done by Guu et al. (2015), we trained TransGaussian (SINGLE) with atomic triplets only and trained TransGaussian (COMP) with the union of atomic triplets and paths. We did not incorporate word embedding in this task and each entity is assigned its individual vector. Without getting parameters tuned too much, TransGaussian (COMP) obtained accuracy comparable to TransE (COMP). See Table 11. ", + "bbox": [ + 174, + 895, + 823, + 924 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/4a25b8273f36037ebd611825cf1990cec4dc4df993551c3f676718009d7fca5b.jpg", + "image_caption": [ + "Figure 4: TransGaussian entity embeddings. Crosses are the subjects and circles are the objects of a relation. Specifically, crosses are players in (a)-(e) and professional football clubs in (f). " + ], + "image_footnote": [], + "bbox": [ + 174, + 97, + 875, + 704 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 775, + 826, + 818 + ], + "page_idx": 14 + }, + { + "type": "table", + "img_path": "images/5fbe82f533094c85145ea099106cb95991607d24b32e7ddd6a941002c8b6ab14.jpg", + "table_caption": [ + "Table 9: Experimental results of path queries on WorldCup2014. " + ], + "table_footnote": [], + "table_body": "
TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#Relation and sample questionMean H@1(%）Filtered RankH@1(%)Mean Filtered RankMean H@1(%) Filtered RankH@1(%)Mean Filtered Rank
1plays.in_club (which club does alan pulido play for?)90.60 1.1292.621.1196.64 1.0397.991.03
2plays-position (what position does gonzalo higuain play?)100.00 1.0098.111.0298.74 1.01100.001.00
3is_aged (how old is samuel etoo?)81.58 1.3092.111.1096.05 1.04100.001.00
4wears_number (what is the jersey number of mario balotelli?)44.29 1.8885.711.1996.43 1.04100.001.00
5plays-for-country (which country is thomas mueller from ?)97.60 1.0294.401.1198.40 1.0299.201.01
6is_in.country (which country is the soccer team fc porto based in ?)98.48 1.0298.481.0293.94 1.0898.481.02
7plays_in_club-1 (who plays professionally at liverpool fc?)95.12 1.0886.991.3896.75 1.0396.751.03
8plays_for_country (which player is from iran?)81.16 1.6172.462.3640.58 3.1993.241.48
9plays-position (name a player who plays goalkeeper?)100.00 1.0030.212.3055.21 5.0985.421.15
10is.in_country (which soccer club is based in mexico?)24.58 11.4723.7310.075.08 9.1817.8020.10
11plays_in_club/is_in_country (where is the club that edin dzeko plays for ?)48.68 4.2462.502.0748.03 2.4176.971.50
12plays-for-country-1/plays-in-club (name a soccer club that hasaplayer from australia ?)34.78 9.4930.4311.266.52 9.8816.3020.27
Overall74.92 2.8074.352.7170.172.82 84.423.68
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TransE(SINGLE)TransE(COMP)TransGaussian(SINGLE)TransGaussian(COMP)
#Relation and sample questionMeanH@1(%)FilteredRankMeanH@1(%)FilteredRankMeanH@1(%)FilteredRankMeanH@1(%)FilteredRank
13(who plays forward for fc barcelona?)94.48 1.1071.17 1.7787.12 1.3798.77 1.02
14plays-position-and plays-for-country-1(who are the defenders on german national team?)95.93 1.0876.42 2.5064.23 2.02100.00 1.00
15plays_in_club-1andis_in_country(which player in ssc napoli is from argentina?)91.79 1.1375.37 1.7588.06 1.3794.03 1.07
Overall94.05 1.1174.05 1.9780.71 1.5697.62 1.03
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ModelAccuracy (%)
TransE (SINGLE)68.5
TransE (COMP)80.3
TransGaussian (SINGLE)58.4
TransGaussian (COMP)76.4
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As we show in Figure 1, we can view the conven-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 379, + 504, + 391 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 504, + 391 + ], + "score": 1.0, + "content": "tional inner-product-based attention and the proposed Gaussian attention as addressing by an affine", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 390, + 505, + 402 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 505, + 402 + ], + "score": 1.0, + "content": "energy function and a quadratic energy function, respectively. 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As we show in Figure 1, we can view the conven-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 379, + 504, + 391 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 504, + 391 + ], + "score": 1.0, + "content": "tional inner-product-based attention and the proposed Gaussian attention as addressing by an affine", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 390, + 505, + 402 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 505, + 402 + ], + "score": 1.0, + "content": "energy function and a quadratic energy function, respectively. By making the addressing mechanism", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 401, + 505, + 414 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 505, + 414 + ], + "score": 1.0, + "content": "more complex, we may represent many entities in a relatively low dimensional embedding space.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 412, + 506, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 506, + 424 + ], + "score": 1.0, + "content": "Since knowledge bases are typically extremely sparse, it is more likely that we can afford to have a", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 424, + 372, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 372, + 435 + ], + "score": 1.0, + "content": "more complex attention model than a large embedding dimension.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 18.5, + "bbox_fs": [ + 104, + 346, + 506, + 435 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 439, + 505, + 495 + ], + "lines": [ + { + "bbox": [ + 106, + 439, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 505, + 452 + ], + "score": 1.0, + "content": "We apply the proposed Gaussian attention model to question answering based on knowledge bases.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 450, + 505, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 505, + 463 + ], + "score": 1.0, + "content": "At the high-level, the goal of the task is to learn the mapping from a question about objects in the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 460, + 506, + 476 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 506, + 476 + ], + "score": 1.0, + "content": "knowledge base in natural language to a probability distribution over the entities. We use the scoring", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 473, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 505, + 484 + ], + "score": 1.0, + "content": "function (1) for both embedding the entities as vectors, and extracting the conditions mentioned in", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 484, + 480, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 480, + 496 + ], + "score": 1.0, + "content": "the question and taking a conjunction of them to score each candidate answer to the question.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25, + "bbox_fs": [ + 105, + 439, + 506, + 496 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 500, + 505, + 567 + ], + "lines": [ + { + "bbox": [ + 106, + 500, + 506, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 500, + 506, + 513 + ], + "score": 1.0, + "content": "The ability to compactly represent a set of objects makes the Gaussian attention model well suited for", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 511, + 505, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 505, + 523 + ], + "score": 1.0, + "content": "representing the uncertainty in a multiple-answer question (e.g., “who are the children of Abraham", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 522, + 505, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 505, + 535 + ], + "score": 1.0, + "content": "Lincoln?”). Moreover, traversal over the knowledge graph (see Guu et al., 2015) can be naturally", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 532, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 505, + 546 + ], + "score": 1.0, + "content": "handled by a series of Gaussian convolutions, which generalizes the addition of vectors. In fact, we", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 545, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 545, + 505, + 556 + ], + "score": 1.0, + "content": "model each relation as a Gaussian with mean and variance parameters. Thus a traversal on a relation", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 555, + 388, + 568 + ], + "spans": [ + { + "bbox": [ + 106, + 555, + 388, + 568 + ], + "score": 1.0, + "content": "corresponds to a translation in the mean and addition of the variances.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 500, + 506, + 568 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 572, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 106, + 572, + 506, + 584 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 506, + 584 + ], + "score": 1.0, + "content": "The proposed question answering model is able to handle not only the case where the answer to a", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 582, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 505, + 595 + ], + "score": 1.0, + "content": "question is associated with an atomic fact, which is called simple Q&A (Bordes et al., 2015), but also", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 594, + 506, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 506, + 607 + ], + "score": 1.0, + "content": "questions that require composition of relations (path queries in Guu et al. (2015)) and conjunction of", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 604, + 506, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 506, + 618 + ], + "score": 1.0, + "content": "queries. An example flow of how our model deals with a question “Who plays forward for Borussia", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 616, + 296, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 296, + 628 + ], + "score": 1.0, + "content": "Dortmund?” is shown in Figure 2 in Section 3.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 36, + "bbox_fs": [ + 105, + 572, + 506, + 628 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 632, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 632, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 505, + 645 + ], + "score": 1.0, + "content": "This paper is structured as follows. In Section 2, we describe how the Gaussian scoring function", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "score": 1.0, + "content": "(1) can be used to embed the entities in a knowledge base into a continuous vector space. We call", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 654, + 504, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 504, + 667 + ], + "score": 1.0, + "content": "our model TransGaussian because of its similarity to the TransE model proposed by Bordes et al.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 665, + 506, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 506, + 679 + ], + "score": 1.0, + "content": "(2013). Then in Section 3, we describe our question answering model. In Section 4, we carry out", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "score": 1.0, + "content": "experiments on WorldCup2014 dataset we collected. The dataset is relatively small but it allows us", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 688, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 504, + 700 + ], + "score": 1.0, + "content": "to evaluate not only simple questions but also path queries and conjunction of queries. The proposed", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "TransGaussian embedding with the question answering model achieves significantly higher accuracy", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "than the vanilla TransE embedding or TransE trained with compositional relations Guu et al. (2015)", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 721, + 316, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 316, + 733 + ], + "score": 1.0, + "content": "combined with the same question answering model.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 43, + "bbox_fs": [ + 105, + 632, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 291, + 94 + ], + "lines": [ + { + "bbox": [ + 105, + 80, + 292, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 292, + 96 + ], + "score": 1.0, + "content": "2 KNOWLEDGE BASE EMBEDDING", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 105, + 505, + 150 + ], + "lines": [ + { + "bbox": [ + 105, + 106, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 106, + 505, + 118 + ], + "score": 1.0, + "content": "In this section, we describe the proposed TransGaussian model based on the Gaussian attention", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 117, + 505, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 117, + 505, + 129 + ], + "score": 1.0, + "content": "model (1). 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A knowledge base is a collec-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 194, + 504, + 207 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 173, + 207 + ], + "score": 1.0, + "content": "tion of triplets", + "type": "text" + }, + { + "bbox": [ + 173, + 195, + 204, + 207 + ], + "score": 0.92, + "content": "( s , r , o )", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 194, + 276, + 207 + ], + "score": 1.0, + "content": ", where we call", + "type": "text" + }, + { + "bbox": [ + 277, + 195, + 311, + 206 + ], + "score": 0.75, + "content": "\\textit { s } \\in \\textit { \\varepsilon }", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 194, + 317, + 207 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 317, + 195, + 353, + 205 + ], + "score": 0.72, + "content": "r \\in \\mathcal { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 194, + 379, + 207 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 380, + 195, + 414, + 205 + ], + "score": 0.89, + "content": "\\textit { o } \\in \\textit { \\mathcal { E } }", + "type": "inline_equation" + }, + { + "bbox": [ + 414, + 194, + 504, + 207 + ], + "score": 1.0, + "content": ", the subject, the re-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 205, + 504, + 219 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 504, + 219 + ], + "score": 1.0, + "content": "lation, and the object of the triplet, respectively. Each triplet encodes a fact. For example,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 217, + 505, + 229 + ], + "spans": [ + { + "bbox": [ + 106, + 217, + 505, + 229 + ], + "score": 1.0, + "content": "(Albert Einstein, has profession, theoretical physicist). All the triplets given", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 227, + 505, + 240 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 505, + 240 + ], + "score": 1.0, + "content": "in a knowledge base are assumed to be true. However generally speaking a triplet may be true or", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 238, + 506, + 251 + ], + "spans": [ + { + "bbox": [ + 105, + 238, + 506, + 251 + ], + "score": 1.0, + "content": "false. Thus knowledge base embedding aims at training a model that predict if a triplet is true or not", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 249, + 506, + 262 + ], + "spans": [ + { + "bbox": [ + 105, + 249, + 506, + 262 + ], + "score": 1.0, + "content": "given some parameterization of the entities and relations (Bordes et al., 2011; 2013; Nickel et al.,", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 261, + 289, + 273 + ], + "spans": [ + { + "bbox": [ + 106, + 261, + 289, + 273 + ], + "score": 1.0, + "content": "2011; Socher et al., 2013; Wang et al., 2014).", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 107, + 277, + 503, + 302 + ], + "lines": [ + { + "bbox": [ + 134, + 276, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 134, + 276, + 220, + 310 + ], + "score": 1.0, + "content": "paper, we associate awith two parameters,", + "type": "text" + }, + { + "bbox": [ + 249, + 276, 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With the scoring function (4), the generalized training objective", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 382, + 504, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 427, + 394 + ], + "score": 1.0, + "content": "for compositional relations can be written identically to (3) except for replacing", + "type": "text" + }, + { + "bbox": [ + 428, + 383, + 437, + 393 + ], + "score": 0.82, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 382, + 459, + 394 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 459, + 383, + 487, + 393 + ], + "score": 0.9, + "content": "\\mathcal { T } \\cup \\mathcal { P }", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 382, + 504, + 394 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 392, + 241, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 146, + 406 + ], + "score": 1.0, + "content": "replacing", + "type": "text" + }, + { + "bbox": [ + 146, + 394, + 156, + 403 + ], + "score": 0.8, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 157, + 392, + 178, + 406 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 178, + 393, + 236, + 406 + ], + "score": 0.93, + "content": "N ^ { \\prime } = | \\mathcal { T } \\cup \\mathcal { P } |", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 392, + 241, + 406 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21 + }, + { + "type": "title", + "bbox": [ + 108, + 420, + 246, + 433 + ], + "lines": [ + { + "bbox": [ + 104, + 418, + 248, + 436 + ], + "spans": [ + { + "bbox": [ + 104, + 418, + 248, + 436 + ], + "score": 1.0, + "content": "3 QUESTION ANSWERING", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 444, + 505, + 576 + ], + "lines": [ + { + "bbox": [ + 106, + 445, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 445, + 505, + 457 + ], + "score": 1.0, + "content": "Given a set of question-answer pairs, in which the question is phrased in natural language and the an-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "score": 1.0, + "content": "swer is an entity in the knowledge base, our goal is to train a model that learns the mapping from the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "score": 1.0, + "content": "question to the correct entity. Our question answering model consists of three steps, entity recog-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 478, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 505, + 489 + ], + "score": 1.0, + "content": "nition, relation composition, and conjunction. We first identify a list of entities mentioned in the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 488, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 505, + 502 + ], + "score": 1.0, + "content": "question (which is assumed to be provided by an oracle in this paper). If the question is “Who plays", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 499, + 505, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 499, + 505, + 512 + ], + "score": 1.0, + "content": "Forward for Borussia Dortmund?” then the list would be [Forward, Borussia Dortmund].", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 510, + 505, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 505, + 523 + ], + "score": 1.0, + "content": "The next step is to predict the path of relations on the knowledgegraph starting from each en-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 521, + 505, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 505, + 535 + ], + "score": 1.0, + "content": "tity in the list extracted in the first step. In the above example, this will be (smooth versions of)", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 532, + 506, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 506, + 545 + ], + "score": 1.0, + "content": "/Forward/position played by/ and /Borussia Dortmund/has player/ predicted", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 543, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 505, + 556 + ], + "score": 1.0, + "content": "as series of Gaussian convolutions. In general, we can have multiple relations appearing in each path.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 554, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 554, + 505, + 567 + ], + "score": 1.0, + "content": "Finally, we take a product of all the Gaussian attentions and renormalize it, which is equivalent to", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 566, + 420, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 566, + 420, + 578 + ], + "score": 1.0, + "content": "Bayes’ rule with independent observations (paths) and a noninformative prior.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30.5 + }, + { + "type": "title", + "bbox": [ + 108, + 589, + 227, + 600 + ], + "lines": [ + { + "bbox": [ + 106, + 589, + 228, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 589, + 228, + 601 + ], + "score": 1.0, + "content": "3.1 ENTITY RECOGNITION", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 107, + 610, + 505, + 676 + ], + "lines": [ + { + "bbox": [ + 106, + 609, + 505, + 622 + ], + "spans": [ + { + "bbox": [ + 106, + 609, + 505, + 622 + ], + "score": 1.0, + "content": "We assume that there is an oracle that provides a list containing all the entities mentioned in the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 621, + 505, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 634 + ], + "score": 1.0, + "content": "question, because (1) a domain specific entity recognizer can be developed efficiently (Williams", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 631, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 631, + 505, + 645 + ], + "score": 1.0, + "content": "et al., 2015) and (2) generally entity recognition is a challenging task and it is beyond the scope", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "score": 1.0, + "content": "of this paper to show whether there is any benefit in training our question answering model jointly", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 653, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 505, + 666 + ], + "score": 1.0, + "content": "with a entity recognizer. 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(2015) has recently shown that training TransE with compositional relations can make", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 182, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 104, + 182, + 505, + 195 + ], + "score": 1.0, + "content": "it competitive to more complex models, although TransE is much simpler compared to for exam-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 192, + 506, + 207 + ], + "spans": [ + { + "bbox": [ + 104, + 192, + 506, + 207 + ], + "score": 1.0, + "content": "ple, neural tensor networks (NTN, Socher et al. (2013)) and TransH Wang et al. (2014). Here,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 205, + 505, + 216 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 446, + 216 + ], + "score": 1.0, + "content": "a compositional relation is a relation that is composed as a series of relations in", + "type": "text" + }, + { + "bbox": [ + 447, + 205, + 456, + 214 + ], + "score": 0.81, + "content": "\\mathcal { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 457, + 205, + 505, + 216 + ], + "score": 1.0, + "content": ", for exam-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 215, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 215, + 506, + 227 + ], + "score": 1.0, + "content": "ple, grand father of can be composed as first applying the parent of relation and then the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 226, + 471, + 238 + ], + "spans": [ + { + "bbox": [ + 106, + 226, + 471, + 238 + ], + "score": 1.0, + "content": "father of relation, which can be seen as a traversal over a path on the knowledge graph.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 8.5, + "bbox_fs": [ + 104, + 170, + 506, + 238 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 243, + 505, + 287 + ], + "lines": [ + { + "bbox": [ + 105, + 243, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 506, + 255 + ], + "score": 1.0, + "content": "TransGaussian model can naturally handle and propagate the uncertainty over such a chain of", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 253, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 505, + 267 + ], + "score": 1.0, + "content": "relations by convolving the Gaussian distributions along the path. That is, the score of an en-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 264, + 123, + 277 + ], + "score": 1.0, + "content": "tity", + "type": "text" + }, + { + "bbox": [ + 124, + 267, + 130, + 275 + ], + "score": 0.7, + "content": "o", + "type": "inline_equation" + }, + { + "bbox": [ + 131, + 264, + 185, + 277 + ], + "score": 1.0, + "content": "to be in the", + "type": "text" + }, + { + "bbox": [ + 185, + 267, + 192, + 275 + ], + "score": 0.76, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 264, + 248, + 277 + ], + "score": 1.0, + "content": "-step relation", + "type": "text" + }, + { + "bbox": [ + 248, + 264, + 307, + 277 + ], + "score": 0.93, + "content": "r _ { 1 } / r _ { 2 } / \\cdots / r _ { \\tau }", + "type": "inline_equation" + }, + { + "bbox": [ + 307, + 264, + 363, + 277 + ], + "score": 1.0, + "content": "with subject", + "type": "text" + }, + { + "bbox": [ + 363, + 267, + 369, + 275 + ], + "score": 0.7, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 370, + 264, + 505, + 277 + ], + "score": 1.0, + "content": ", which we denote by the triplet", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 107, + 275, + 240, + 289 + ], + "spans": [ + { + "bbox": [ + 107, + 275, + 190, + 288 + ], + "score": 0.91, + "content": "( \\dot { s , } r _ { 1 } / r _ { 2 } / \\cdot \\cdot \\cdot / r _ { \\tau } , o )", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 276, + 240, + 289 + ], + "score": 1.0, + "content": ", is given as", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 243, + 506, + 289 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 182, + 289, + 426, + 302 + ], + "lines": [ + { + "bbox": [ + 182, + 289, + 426, + 302 + ], + "spans": [ + { + "bbox": [ + 182, + 289, + 426, + 302 + ], + "score": 0.84, + "content": "\\begin{array} { r } { \\mathrm { s c o r e } ( s , r _ { 1 } / r _ { 2 } / \\cdot \\cdot \\cdot / r _ { \\tau } , o ) = \\log \\phi ( \\pmb { v } _ { o } | \\pmb { \\mu } _ { \\mathrm { c o n t e x t } } , \\pmb { \\Sigma } _ { \\mathrm { c o n t e x t } } ) , } \\end{array}", + "type": "interline_equation", + "image_path": "cb93d0b8c285b8098298d11c8377beb8dea13fa379d403f59d98150719afc4c2.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 182, + 289, + 426, + 302 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 304, + 508, + 328 + ], + "lines": [ + { + "bbox": [ + 103, + 300, + 507, + 322 + ], + "spans": [ + { + "bbox": [ + 103, + 300, + 127, + 322 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 128, + 304, + 244, + 317 + ], + "score": 0.91, + "content": "\\begin{array} { r } { \\pmb { \\mu } _ { \\mathrm { c o n t e x t } } = \\pmb { v } _ { s } + \\sum _ { t = 1 } ^ { \\tau } \\delta _ { r _ { t } } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 300, + 249, + 322 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 249, + 304, + 346, + 317 + ], + "score": 0.88, + "content": "\\begin{array} { r } { \\sum _ { \\mathrm { c o n t e x t } } = \\sum _ { t = 1 } ^ { \\tau } \\sum _ { r _ { t } } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 346, + 300, + 507, + 322 + ], + "score": 1.0, + "content": ", where the covariance associated with", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 316, + 414, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 316, + 414, + 329 + ], + "score": 1.0, + "content": "each relation is parameterized in the same way as in the previous subsection.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17.5, + "bbox_fs": [ + 103, + 300, + 507, + 329 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 341, + 505, + 405 + ], + "lines": [ + { + "bbox": [ + 100, + 337, + 506, + 367 + ], + "spans": [ + { + "bbox": [ + 100, + 337, + 457, + 367 + ], + "score": 1.0, + "content": "Training with compositional relations Let P = n\u0010si, ri1 /ri2 / · · · /rili , oi\u0011oN i=1", + "type": "text" + }, + { + "bbox": [ + 455, + 344, + 506, + 358 + ], + "score": 1.0, + "content": "be a set of", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 360, + 505, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 374, + 373 + ], + "score": 1.0, + "content": "randomly sampled paths from the knowledge graph. Here relation", + "type": "text" + }, + { + "bbox": [ + 374, + 363, + 387, + 373 + ], + "score": 0.84, + "content": "r _ { i _ { k } }", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 360, + 505, + 373 + ], + "score": 1.0, + "content": "in a path can be a relation in", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 107, + 370, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 107, + 372, + 117, + 381 + ], + "score": 0.81, + "content": "\\mathcal { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 117, + 370, + 217, + 384 + ], + "score": 1.0, + "content": "or an inverse relation in", + "type": "text" + }, + { + "bbox": [ + 218, + 371, + 238, + 382 + ], + "score": 0.91, + "content": "\\mathcal { R } ^ { - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 238, + 370, + 505, + 384 + ], + "score": 1.0, + "content": ". With the scoring function (4), the generalized training objective", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 382, + 504, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 427, + 394 + ], + "score": 1.0, + "content": "for compositional relations can be written identically to (3) except for replacing", + "type": "text" + }, + { + "bbox": [ + 428, + 383, + 437, + 393 + ], + "score": 0.82, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 382, + 459, + 394 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 459, + 383, + 487, + 393 + ], + "score": 0.9, + "content": "\\mathcal { T } \\cup \\mathcal { P }", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 382, + 504, + 394 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 392, + 241, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 146, + 406 + ], + "score": 1.0, + "content": "replacing", + "type": "text" + }, + { + "bbox": [ + 146, + 394, + 156, + 403 + ], + "score": 0.8, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 157, + 392, + 178, + 406 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 178, + 393, + 236, + 406 + ], + "score": 0.93, + "content": "N ^ { \\prime } = | \\mathcal { T } \\cup \\mathcal { P } |", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 392, + 241, + 406 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21, + "bbox_fs": [ + 100, + 337, + 506, + 406 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 420, + 246, + 433 + ], + "lines": [ + { + "bbox": [ + 104, + 418, + 248, + 436 + ], + "spans": [ + { + "bbox": [ + 104, + 418, + 248, + 436 + ], + "score": 1.0, + "content": "3 QUESTION ANSWERING", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 444, + 505, + 576 + ], + "lines": [ + { + "bbox": [ + 106, + 445, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 445, + 505, + 457 + ], + "score": 1.0, + "content": "Given a set of question-answer pairs, in which the question is phrased in natural language and the an-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "score": 1.0, + "content": "swer is an entity in the knowledge base, our goal is to train a model that learns the mapping from the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "score": 1.0, + "content": "question to the correct entity. Our question answering model consists of three steps, entity recog-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 478, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 505, + 489 + ], + "score": 1.0, + "content": "nition, relation composition, and conjunction. We first identify a list of entities mentioned in the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 488, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 505, + 502 + ], + "score": 1.0, + "content": "question (which is assumed to be provided by an oracle in this paper). If the question is “Who plays", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 499, + 505, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 499, + 505, + 512 + ], + "score": 1.0, + "content": "Forward for Borussia Dortmund?” then the list would be [Forward, Borussia Dortmund].", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 510, + 505, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 505, + 523 + ], + "score": 1.0, + "content": "The next step is to predict the path of relations on the knowledgegraph starting from each en-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 521, + 505, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 505, + 535 + ], + "score": 1.0, + "content": "tity in the list extracted in the first step. In the above example, this will be (smooth versions of)", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 532, + 506, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 506, + 545 + ], + "score": 1.0, + "content": "/Forward/position played by/ and /Borussia Dortmund/has player/ predicted", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 543, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 505, + 556 + ], + "score": 1.0, + "content": "as series of Gaussian convolutions. In general, we can have multiple relations appearing in each path.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 554, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 554, + 505, + 567 + ], + "score": 1.0, + "content": "Finally, we take a product of all the Gaussian attentions and renormalize it, which is equivalent to", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 566, + 420, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 566, + 420, + 578 + ], + "score": 1.0, + "content": "Bayes’ rule with independent observations (paths) and a noninformative prior.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 445, + 506, + 578 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 589, + 227, + 600 + ], + "lines": [ + { + "bbox": [ + 106, + 589, + 228, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 589, + 228, + 601 + ], + "score": 1.0, + "content": "3.1 ENTITY RECOGNITION", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 107, + 610, + 505, + 676 + ], + "lines": [ + { + "bbox": [ + 106, + 609, + 505, + 622 + ], + "spans": [ + { + "bbox": [ + 106, + 609, + 505, + 622 + ], + "score": 1.0, + "content": "We assume that there is an oracle that provides a list containing all the entities mentioned in the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 621, + 505, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 634 + ], + "score": 1.0, + "content": "question, because (1) a domain specific entity recognizer can be developed efficiently (Williams", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 631, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 631, + 505, + 645 + ], + "score": 1.0, + "content": "et al., 2015) and (2) generally entity recognition is a challenging task and it is beyond the scope", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "score": 1.0, + "content": "of this paper to show whether there is any benefit in training our question answering model jointly", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 653, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 505, + 666 + ], + "score": 1.0, + "content": "with a entity recognizer. 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Two entities Forward and", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 319, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 106, + 319, + 505, + 330 + ], + "score": 1.0, + "content": "Borussia Dortmund are identified in the question and associated with point mass distributions", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 329, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 329, + 505, + 342 + ], + "score": 1.0, + "content": "centered at the corresponding entity vectors. An LSTM encodes the input into a sequence of output", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 340, + 505, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 473, + 353 + ], + "score": 1.0, + "content": "vectors of the same length. 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Accordingly, the score for each candidate", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 673, + 266, + 685 + ], + "spans": [ + { + "bbox": [ + 106, + 673, + 137, + 685 + ], + "score": 1.0, + "content": "answer", + "type": "text" + }, + { + "bbox": [ + 137, + 675, + 144, + 683 + ], + "score": 0.63, + "content": "o", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 673, + 266, + 685 + ], + "score": 1.0, + "content": "can be expressed using (1) as:", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26.5 + }, + { + "type": "interline_equation", + "bbox": [ + 221, + 688, + 389, + 703 + ], + "lines": [ + { + "bbox": [ + 221, + 688, + 389, + 703 + ], + "spans": [ + { + "bbox": [ + 221, + 688, + 389, + 703 + ], + "score": 0.92, + "content": "\\mathrm { s c o r e } _ { e } ( \\pmb { v } _ { o } ) = \\log \\phi ( \\pmb { v } _ { o } | \\pmb { \\mu } _ { e , \\alpha , \\mathrm { K B } } , \\pmb { \\Sigma } _ { e , \\alpha , \\mathrm { K B } } )", + "type": "interline_equation", + "image_path": "2bda7cc08ca20184c9dd2f7776ba0063ba8e71d48f6c8123f749f089080f9874.jpg" + } + ] + } + ], + "index": 29, + "virtual_lines": [ + { + "bbox": [ + 221, + 688, + 389, + 703 + ], + "spans": [], + "index": 29 + } + ] + }, + { + "type": "text", + "bbox": [ + 109, + 706, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 705, + 507, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 705, + 127, + 723 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 127, + 707, + 363, + 721 + ], + "score": 0.76, + "content": "\\begin{array} { r } { \\pmb { \\mu } _ { e , \\alpha , \\mathrm { K B } } = \\pmb { v } _ { e } + \\sum _ { r \\in \\bar { \\mathcal { R } } } \\alpha _ { r , e } \\delta _ { r } , \\sum _ { e , \\alpha , \\mathrm { K B } } = \\sum _ { r \\in \\bar { \\mathcal { R } } } \\alpha _ { r , e } ^ { 2 } \\pmb { \\Sigma } _ { r } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 364, + 705, + 396, + 723 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 396, + 709, + 407, + 718 + ], + "score": 0.86, + "content": "{ \\pmb v } _ { e }", + "type": "inline_equation" + }, + { + "bbox": [ + 407, + 705, + 507, + 723 + ], + "score": 1.0, + "content": "is the vector associated", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 717, + 472, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 717, + 152, + 734 + ], + "score": 1.0, + "content": "with entity", + "type": "text" + }, + { + "bbox": [ + 152, + 723, + 158, + 730 + ], + "score": 0.75, + "content": "e", + "type": "inline_equation" + }, + { + "bbox": [ + 158, + 717, + 176, + 734 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 176, + 720, + 237, + 731 + ], + "score": 0.9, + "content": "\\bar { \\mathcal { R } } = \\mathcal { R } \\cup \\mathcal { R } ^ { - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 717, + 472, + 734 + ], + "score": 1.0, + "content": "denotes the set of relations including the inverse relations.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30.5 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 82, + 511, + 298 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 107, + 82, + 511, + 298 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 82, + 511, + 298 + ], + "spans": [ + { + "bbox": [ + 107, + 82, + 511, + 298 + ], + "score": 0.972, + "type": "image", + "image_path": "c8be4c487573afc71d590a3b723235da8f6bd144ebef356a786893ec5f627b32.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 107, + 82, + 511, + 154.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 107, + 154.0, + 511, + 226.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 107, + 226.0, + 511, + 298.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 306, + 506, + 396 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 307, + 506, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 307, + 506, + 320 + ], + "score": 1.0, + "content": "Figure 2: The input to the system is a question in natural language. 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Here", + "type": "text" + }, + { + "bbox": [ + 362, + 211, + 371, + 220 + ], + "score": 0.8, + "content": "\\Theta", + "type": "inline_equation" + }, + { + "bbox": [ + 371, + 210, + 505, + 223 + ], + "score": 1.0, + "content": "denotes all the parameters of the", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 222, + 217, + 234 + ], + "spans": [ + { + "bbox": [ + 106, + 222, + 217, + 234 + ], + "score": 1.0, + "content": "question-answering model.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8 + }, + { + "type": "title", + "bbox": [ + 107, + 245, + 329, + 257 + ], + "lines": [ + { + "bbox": [ + 106, + 245, + 331, + 258 + ], + "spans": [ + { + "bbox": [ + 106, + 245, + 331, + 258 + ], + "score": 1.0, + "content": "3.4 TRAINING THE QUESTION ANSWERING MODEL", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 265, + 505, + 334 + ], + "lines": [ + { + "bbox": [ + 106, + 264, + 506, + 279 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 289, + 279 + ], + "score": 1.0, + "content": "Suppose we have a knowledge base", + "type": "text" + }, + { + "bbox": [ + 289, + 266, + 329, + 278 + ], + "score": 0.92, + "content": "( \\mathcal { E } , \\mathcal { R } , \\mathcal { T } )", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 264, + 506, + 279 + ], + "score": 1.0, + "content": "and a trained TransGaussian model", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 108, + 276, + 506, + 293 + ], + "spans": [ + { + "bbox": [ + 108, + 277, + 217, + 291 + ], + "score": 0.91, + "content": "\\big ( \\{ v _ { e } \\} _ { e \\in \\mathcal { E } } , \\{ ( \\delta _ { r } , \\Sigma _ { r } ) \\} _ { r \\in \\bar { \\mathcal { R } } } \\big )", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 276, + 255, + 293 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 256, + 277, + 266, + 288 + ], + "score": 0.83, + "content": "\\bar { \\mathcal { R } }", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 276, + 506, + 293 + ], + "score": 1.0, + "content": "is the set of all relations including the inverse rela-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 288, + 506, + 303 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 506, + 303 + ], + "score": 1.0, + "content": "tions. 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We assume that the number of relations implied", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 465, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 465, + 505, + 477 + ], + "score": 1.0, + "content": "in a question is small compared to the total number of relations in the knowledge base. Hence the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 476, + 433, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 155, + 488 + ], + "score": 1.0, + "content": "coefficients", + "type": "text" + }, + { + "bbox": [ + 155, + 478, + 172, + 488 + ], + "score": 0.87, + "content": "\\alpha _ { r , e }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 477, + 286, + 488 + ], + "score": 1.0, + "content": "computed for each question", + "type": "text" + }, + { + "bbox": [ + 286, + 478, + 295, + 487 + ], + "score": 0.83, + "content": "q _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 296, + 477, + 392, + 488 + ], + "score": 1.0, + "content": "are regularized by their", + "type": "text" + }, + { + "bbox": [ + 392, + 476, + 402, + 487 + ], + "score": 0.86, + "content": "\\ell _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 477, + 433, + 488 + ], + "score": 1.0, + "content": "norms.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26.5 + }, + { + "type": "title", + "bbox": [ + 108, + 503, + 200, + 515 + ], + "lines": [ + { + "bbox": [ + 105, + 502, + 201, + 517 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 201, + 517 + ], + "score": 1.0, + "content": "4 EXPERIMENTS", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 107, + 526, + 505, + 626 + ], + "lines": [ + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "As a demonstration of the proposed framework, we perform question and answering on a dataset", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "score": 1.0, + "content": "of soccer players. In this work, we consider two types of questions. A path query is a question", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "score": 1.0, + "content": "that contains only one named entity from the knowledge base and its answer can be found from", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 104, + 559, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 104, + 559, + 506, + 574 + ], + "score": 1.0, + "content": "the knowledge graph by walking down a path consisting of a few relations. A conjunctive query", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 571, + 506, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 571, + 506, + 583 + ], + "score": 1.0, + "content": "is a question that contains more than one entities and the answer is given as the conjunction of", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 581, + 506, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 581, + 506, + 595 + ], + "score": 1.0, + "content": "all path queries starting from each entity. Furthermore, we experimented on a knowledge base", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 593, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 593, + 505, + 605 + ], + "score": 1.0, + "content": "completion task with TransGaussian embeddings to test its capability of generalization to unseen", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 603, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 603, + 505, + 617 + ], + "score": 1.0, + "content": "fact. Since knowledge base completion is not the main focus of this work, we include the results in", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 615, + 165, + 627 + ], + "spans": [ + { + "bbox": [ + 106, + 615, + 165, + 627 + ], + "score": 1.0, + "content": "the Appendix.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 34 + }, + { + "type": "title", + "bbox": [ + 108, + 639, + 246, + 650 + ], + "lines": [ + { + "bbox": [ + 105, + 637, + 249, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 249, + 651 + ], + "score": 1.0, + "content": "4.1 WORLDCUP2014 DATASET", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 39 + }, + { + "type": "text", + "bbox": [ + 107, + 659, + 504, + 714 + ], + "lines": [ + { + "bbox": [ + 106, + 658, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 106, + 658, + 505, + 671 + ], + "score": 1.0, + "content": "We build a knowledge base of football players that participated in FIFA World Cup", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 668, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 505, + 683 + ], + "score": 1.0, + "content": "2014 1. The original dataset consists of players’ information such as nationality, posi-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 680, + 505, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 680, + 505, + 694 + ], + "score": 1.0, + "content": "tions on the field and ages etc. We picked a few attributes and constructed 1127 en-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 691, + 505, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 691, + 505, + 705 + ], + "score": 1.0, + "content": "tities and 6 atomic relations. The entities include 736 players, 297 professional soc-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 702, + 505, + 716 + ], + "spans": [ + { + "bbox": [ + 105, + 702, + 505, + 716 + ], + "score": 1.0, + "content": "cer clubs, 51 countries, 39 numbers and 4 positions. And the six atomic relations are", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 42 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 26, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 118, + 721, + 462, + 731 + ], + "lines": [ + { + "bbox": [ + 119, + 719, + 464, + 735 + ], + "spans": [ + { + "bbox": [ + 119, + 719, + 464, + 735 + ], + "score": 1.0, + "content": "1The original dataset can be found at https://datahub.io/dataset/fifa-world-cup-2014-all-players.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 310, + 762 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 82, + 195, + 93 + ], + "lines": [ + { + "bbox": [ + 104, + 80, + 196, + 96 + ], + "spans": [ + { + "bbox": [ + 104, + 80, + 196, + 96 + ], + "score": 1.0, + "content": "3.3 CONJUNCTION", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 102, + 505, + 136 + ], + "lines": [ + { + "bbox": [ + 105, + 103, + 505, + 115 + ], + "spans": [ + { + "bbox": [ + 105, + 103, + 122, + 115 + ], + "score": 1.0, + "content": "Let", + "type": "text" + }, + { + "bbox": [ + 122, + 103, + 142, + 115 + ], + "score": 0.92, + "content": "\\mathcal { E } ( q )", + "type": "inline_equation" + }, + { + "bbox": [ + 142, + 103, + 331, + 115 + ], + "score": 1.0, + "content": "be the set of entities recognized in the question", + "type": "text" + }, + { + "bbox": [ + 332, + 105, + 338, + 115 + ], + "score": 0.8, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 103, + 505, + 115 + ], + "score": 1.0, + "content": ". The final step of our model is to take the", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 113, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 113, + 505, + 127 + ], + "score": 1.0, + "content": "conjunction of the Gaussian attentions derived in the previous step. This step is simply carried out", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 125, + 309, + 137 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 309, + 137 + ], + "score": 1.0, + "content": "by multiplying the Gaussian attentions as follows:", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2, + "bbox_fs": [ + 105, + 103, + 505, + 137 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 137, + 137, + 473, + 199 + ], + "lines": [ + { + "bbox": [ + 137, + 137, + 473, + 199 + ], + "spans": [ + { + "bbox": [ + 137, + 137, + 473, + 199 + ], + "score": 0.94, + "content": "\\begin{array} { r l } & { \\mathrm { s c o r e } ( \\pmb { v } _ { o } | \\mathcal { E } ( q ) , \\Theta ) = \\underset { e \\in \\mathcal { E } ( q ) } { \\log \\prod } \\phi ( \\pmb { v } _ { o } | \\pmb { \\mu } _ { e , \\alpha , \\mathrm { K B } } , \\pmb { \\Sigma } _ { e , \\alpha , \\mathrm { K B } } ) } \\\\ & { \\qquad = - \\cfrac { 1 } { 2 } \\displaystyle \\sum _ { e \\in \\mathcal { E } ( q ) } \\left( \\pmb { v } _ { o } - \\pmb { \\mu } _ { e , \\alpha , \\mathrm { K B } } \\right) ^ { \\top } \\pmb { \\Sigma } _ { e , \\alpha , \\mathrm { K B } } ^ { - 1 } ( \\pmb { v } _ { o } - \\pmb { \\mu } _ { e , \\alpha , \\mathrm { K B } } ) + \\mathrm { c o n s t . } , } \\end{array}", + "type": "interline_equation", + "image_path": "7a525619e51c23780d45b9a7021f18a63cee7243fd7e4bee1093ec968f13bce2.jpg" + } + ] + } + ], + "index": 5, + "virtual_lines": [ + { + "bbox": [ + 137, + 137, + 473, + 157.66666666666666 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 137, + 157.66666666666666, + 473, + 178.33333333333331 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 137, + 178.33333333333331, + 473, + 198.99999999999997 + ], + "spans": [], + "index": 6 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 199, + 505, + 233 + ], + "lines": [ + { + "bbox": [ + 104, + 198, + 506, + 214 + ], + "spans": [ + { + "bbox": [ + 104, + 198, + 367, + 214 + ], + "score": 1.0, + "content": "which is again a (logarithm of) Gaussian scoring function, where", + "type": "text" + }, + { + "bbox": [ + 367, + 201, + 399, + 212 + ], + "score": 0.89, + "content": "\\mu _ { e , \\alpha , \\mathrm { K B } }", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 198, + 417, + 214 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 417, + 200, + 450, + 212 + ], + "score": 0.92, + "content": "\\Sigma _ { e , \\alpha , \\mathrm { K B } }", + "type": "inline_equation" + }, + { + "bbox": [ + 451, + 198, + 506, + 214 + ], + "score": 1.0, + "content": "are the mean", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 210, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 210, + 361, + 223 + ], + "score": 1.0, + "content": "and the covariance of the Gaussian attention given in (6). Here", + "type": "text" + }, + { + "bbox": [ + 362, + 211, + 371, + 220 + ], + "score": 0.8, + "content": "\\Theta", + "type": "inline_equation" + }, + { + "bbox": [ + 371, + 210, + 505, + 223 + ], + "score": 1.0, + "content": "denotes all the parameters of the", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 222, + 217, + 234 + ], + "spans": [ + { + "bbox": [ + 106, + 222, + 217, + 234 + ], + "score": 1.0, + "content": "question-answering model.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8, + "bbox_fs": [ + 104, + 198, + 506, + 234 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 245, + 329, + 257 + ], + "lines": [ + { + "bbox": [ + 106, + 245, + 331, + 258 + ], + "spans": [ + { + "bbox": [ + 106, + 245, + 331, + 258 + ], + "score": 1.0, + "content": "3.4 TRAINING THE QUESTION ANSWERING MODEL", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 265, + 505, + 334 + ], + "lines": [ + { + "bbox": [ + 106, + 264, + 506, + 279 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 289, + 279 + ], + "score": 1.0, + "content": "Suppose we have a knowledge base", + "type": "text" + }, + { + "bbox": [ + 289, + 266, + 329, + 278 + ], + "score": 0.92, + "content": "( \\mathcal { E } , \\mathcal { R } , \\mathcal { T } )", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 264, + 506, + 279 + ], + "score": 1.0, + "content": "and a trained TransGaussian model", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 108, + 276, + 506, + 293 + ], + "spans": [ + { + "bbox": [ + 108, + 277, + 217, + 291 + ], + "score": 0.91, + "content": "\\big ( \\{ v _ { e } \\} _ { e \\in \\mathcal { E } } , \\{ ( \\delta _ { r } , \\Sigma _ { r } ) \\} _ { r \\in \\bar { \\mathcal { R } } } \\big )", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 276, + 255, + 293 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 256, + 277, + 266, + 288 + ], + "score": 0.83, + "content": "\\bar { \\mathcal { R } }", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 276, + 506, + 293 + ], + "score": 1.0, + "content": "is the set of all relations including the inverse rela-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 288, + 506, + 303 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 506, + 303 + ], + "score": 1.0, + "content": "tions. During training time, we assume the training set is a supervised question-answer pairs", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 107, + 299, + 504, + 312 + ], + "spans": [ + { + "bbox": [ + 107, + 300, + 243, + 312 + ], + "score": 0.92, + "content": "\\{ ( q _ { i } , \\mathcal { E } ( q _ { i } ) , a _ { i } \\bar { ) } : i = 1 , 2 , . . . , m \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 243, + 299, + 271, + 312 + ], + "score": 1.0, + "content": ". 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For example, on a knowledge base of soccer players, a valid training sample could be", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 264, + 506, + 334 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 338, + 511, + 351 + ], + "lines": [ + { + "bbox": [ + 106, + 337, + 513, + 352 + ], + "spans": [ + { + "bbox": [ + 106, + 337, + 513, + 352 + ], + "score": 1.0, + "content": "(“Who plays forward for Borussia Dortmund?”,[Forward, Borussia Dortmund], Marco Reus).", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17, + "bbox_fs": [ + 106, + 337, + 513, + 352 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 355, + 507, + 390 + ], + "lines": [ + { + "bbox": [ + 106, + 356, + 505, + 368 + ], + "spans": [ + { + "bbox": [ + 106, + 356, + 408, + 368 + ], + "score": 1.0, + "content": "Note that the answer to a question is not necessarily unique and we allow", + "type": "text" + }, + { + "bbox": [ + 408, + 358, + 418, + 366 + ], + "score": 0.86, + "content": "a _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 419, + 356, + 505, + 368 + ], + "score": 1.0, + "content": "to be any of the true", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 367, + 505, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 390, + 379 + ], + "score": 1.0, + "content": "answers in the knowledge base. 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We assume that the number of relations implied", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 465, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 465, + 505, + 477 + ], + "score": 1.0, + "content": "in a question is small compared to the total number of relations in the knowledge base. Hence the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 476, + 433, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 155, + 488 + ], + "score": 1.0, + "content": "coefficients", + "type": "text" + }, + { + "bbox": [ + 155, + 478, + 172, + 488 + ], + "score": 0.87, + "content": "\\alpha _ { r , e }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 477, + 286, + 488 + ], + "score": 1.0, + "content": "computed for each question", + "type": "text" + }, + { + "bbox": [ + 286, + 478, + 295, + 487 + ], + "score": 0.83, + "content": "q _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 296, + 477, + 392, + 488 + ], + "score": 1.0, + "content": "are regularized by their", + "type": "text" + }, + { + "bbox": [ + 392, + 476, + 402, + 487 + ], + "score": 0.86, + "content": "\\ell _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 477, + 433, + 488 + ], + "score": 1.0, + "content": "norms.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26.5, + "bbox_fs": [ + 105, + 442, + 507, + 488 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 503, + 200, + 515 + ], + "lines": [ + { + "bbox": [ + 105, + 502, + 201, + 517 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 201, + 517 + ], + "score": 1.0, + "content": "4 EXPERIMENTS", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 107, + 526, + 505, + 626 + ], + "lines": [ + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "As a demonstration of the proposed framework, we perform question and answering on a dataset", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "score": 1.0, + "content": "of soccer players. In this work, we consider two types of questions. A path query is a question", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "score": 1.0, + "content": "that contains only one named entity from the knowledge base and its answer can be found from", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 104, + 559, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 104, + 559, + 506, + 574 + ], + "score": 1.0, + "content": "the knowledge graph by walking down a path consisting of a few relations. A conjunctive query", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 571, + 506, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 571, + 506, + 583 + ], + "score": 1.0, + "content": "is a question that contains more than one entities and the answer is given as the conjunction of", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 581, + 506, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 581, + 506, + 595 + ], + "score": 1.0, + "content": "all path queries starting from each entity. Furthermore, we experimented on a knowledge base", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 593, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 593, + 505, + 605 + ], + "score": 1.0, + "content": "completion task with TransGaussian embeddings to test its capability of generalization to unseen", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 603, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 603, + 505, + 617 + ], + "score": 1.0, + "content": "fact. Since knowledge base completion is not the main focus of this work, we include the results in", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 615, + 165, + 627 + ], + "spans": [ + { + "bbox": [ + 106, + 615, + 165, + 627 + ], + "score": 1.0, + "content": "the Appendix.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 34, + "bbox_fs": [ + 104, + 527, + 506, + 627 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 639, + 246, + 650 + ], + "lines": [ + { + "bbox": [ + 105, + 637, + 249, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 249, + 651 + ], + "score": 1.0, + "content": "4.1 WORLDCUP2014 DATASET", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 39 + }, + { + "type": "text", + "bbox": [ + 107, + 659, + 504, + 714 + ], + "lines": [ + { + "bbox": [ + 106, + 658, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 106, + 658, + 505, + 671 + ], + "score": 1.0, + "content": "We build a knowledge base of football players that participated in FIFA World Cup", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 668, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 505, + 683 + ], + "score": 1.0, + "content": "2014 1. The original dataset consists of players’ information such as nationality, posi-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 680, + 505, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 680, + 505, + 694 + ], + "score": 1.0, + "content": "tions on the field and ages etc. We picked a few attributes and constructed 1127 en-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 691, + 505, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 691, + 505, + 705 + ], + "score": 1.0, + "content": "tities and 6 atomic relations. The entities include 736 players, 297 professional soc-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 702, + 505, + 716 + ], + "spans": [ + { + "bbox": [ + 105, + 702, + 505, + 716 + ], + "score": 1.0, + "content": "cer clubs, 51 countries, 39 numbers and 4 positions. And the six atomic relations are", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 111, + 80, + 275, + 92 + ], + "spans": [ + { + "bbox": [ + 111, + 80, + 230, + 92 + ], + "score": 1.0, + "content": "plays in club: PLAYER", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 231, + 81, + 272, + 91 + ], + "score": 0.3, + "content": " \\mathrm { C L U B }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 272, + 80, + 275, + 92 + ], + "score": 1.0, + "content": ",", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 111, + 91, + 259, + 104 + ], + "spans": [ + { + "bbox": [ + 111, + 91, + 197, + 104 + ], + "score": 1.0, + "content": "is aged: PLAYER", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 198, + 93, + 210, + 102 + ], + "score": 0.82, + "content": "", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 211, + 91, + 259, + 104 + ], + "score": 1.0, + "content": 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], + "score": 1.0, + "content": "POSITION,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 329, + 90, + 514, + 104 + ], + "spans": [ + { + "bbox": [ + 329, + 90, + 451, + 104 + ], + "score": 1.0, + "content": "wears number 2: PLAYER", + "type": "text" + }, + { + "bbox": [ + 452, + 93, + 464, + 102 + ], + "score": 0.82, + "content": "", + "type": "inline_equation" + }, + { + "bbox": [ + 465, + 90, + 514, + 104 + ], + "score": 1.0, + "content": "NUMBER,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 330, + 103, + 502, + 115 + ], + "spans": [ + { + "bbox": [ + 330, + 103, + 437, + 115 + ], + "score": 1.0, + "content": "is in country: CLUB", + "type": "text" + }, + { + "bbox": [ + 437, + 104, + 451, + 113 + ], + "score": 0.8, + "content": "", + "type": "inline_equation" + }, + { + "bbox": [ + 451, + 103, + 502, + 115 + ], + "score": 1.0, + "content": "COUNTRY,", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 108, + 114, + 506, + 147 + ], + "lines": [ + { + "bbox": [ + 106, + 113, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 106, + 113, + 506, + 127 + ], + "score": 1.0, + "content": "where PLAYER, CLUB, NUMBER, etc, denote the type of entities that can appear as the left or", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 124, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 124, + 506, + 139 + ], + "score": 1.0, + "content": "right argument for each relation. Some relations share the same type as the right argument, e.g.,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 136, + 302, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 136, + 302, + 149 + ], + "score": 1.0, + "content": "plays for country and is in country.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 153, + 505, + 208 + ], + "lines": [ + { + "bbox": [ + 106, + 152, + 505, + 164 + ], + "spans": [ + { + "bbox": [ + 106, + 152, + 505, + 164 + ], + "score": 1.0, + "content": "Given the entities and relations, we transformed the dataset into a set of 3977 triplets. A list of", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 163, + 505, + 176 + ], + "spans": [ + { + "bbox": [ + 105, + 163, + 505, + 176 + ], + "score": 1.0, + "content": "sample triplets can be found in the Appendix. Based on these triplets, we created two sets of question", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 174, + 505, + 188 + ], + "spans": [ + { + "bbox": [ + 105, + 174, + 505, + 188 + ], + "score": 1.0, + "content": "answering tasks which we call path query and conjunctive query respectively. The answer of every", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 185, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 505, + 200 + ], + "score": 1.0, + "content": "question is always an entity in the knowledge base and a question can involve one or two triplets.", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 196, + 266, + 210 + ], + "spans": [ + { + "bbox": [ + 106, + 196, + 266, + 210 + ], + "score": 1.0, + "content": "The questions are generated as follows.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 106, + 221, + 505, + 352 + ], + "lines": [ + { + "bbox": [ + 104, + 219, + 506, + 233 + ], + "spans": [ + { + "bbox": [ + 104, + 219, + 506, + 233 + ], + "score": 1.0, + "content": "Path queries. Among the paths on the knowledge graph, there are some natural composition of", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 232, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 232, + 304, + 244 + ], + "score": 1.0, + "content": "relations, e.g., plays in country (PLAYER", + "type": "text" + }, + { + "bbox": [ + 304, + 232, + 318, + 242 + ], + "score": 0.78, + "content": "", + "type": "inline_equation" + }, + { + "bbox": [ + 319, + 232, + 505, + 244 + ], + "score": 1.0, + "content": "COUNTRY) can be decomposed as the com-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 242, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 261, + 255 + ], + "score": 1.0, + "content": "position of plays in club (PLAYE", + "type": "text" + }, + { + "bbox": [ + 262, + 243, + 296, + 253 + ], + "score": 0.34, + "content": "\\mathbf { R } \\to \\mathbf { C L } ", + "type": "inline_equation" + }, + { + "bbox": [ + 297, + 242, + 406, + 255 + ], + "score": 1.0, + "content": "UB) and is in country", + "type": "text" + }, + { + "bbox": [ + 406, + 243, + 501, + 253 + ], + "score": 0.59, + "content": "( \\mathbf { C L U B } \\to \\mathbf { C O U N T R Y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 242, + 505, + 255 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 254, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 505, + 266 + ], + "score": 1.0, + "content": "In addition to the atomic relations, we manually picked a few meaningful compositions of relations", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 264, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 334, + 277 + ], + "score": 1.0, + "content": "and formed query templates, which takes the form “find", + "type": "text" + }, + { + "bbox": [ + 334, + 264, + 360, + 275 + ], + "score": 0.9, + "content": "e \\in { \\mathcal { E } }", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 264, + 403, + 277 + ], + "score": 1.0, + "content": ", such that", + "type": "text" + }, + { + "bbox": [ + 403, + 264, + 434, + 276 + ], + "score": 0.93, + "content": "( s , p , e )", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 264, + 497, + 277 + ], + "score": 1.0, + "content": "is true”, where", + "type": "text" + }, + { + "bbox": [ + 498, + 266, + 504, + 274 + ], + "score": 0.48, + "content": "s", + "type": "inline_equation" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 275, + 505, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 177, + 287 + ], + "score": 1.0, + "content": "is the subject and", + "type": "text" + }, + { + "bbox": [ + 177, + 277, + 184, + 287 + ], + "score": 0.8, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 185, + 275, + 505, + 287 + ], + "score": 1.0, + "content": "can be an atomic relation or a path of relations. To formulate a set of path-based", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 287, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 505, + 299 + ], + "score": 1.0, + "content": "question-answer pairs, we manually created one or more question templates for every query tem-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 297, + 506, + 310 + ], + "spans": [ + { + "bbox": [ + 104, + 297, + 506, + 310 + ], + "score": 1.0, + "content": "plate (see Table 5) Then, for a particular instantiation of a query template with subject and object", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 308, + 506, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 506, + 322 + ], + "score": 1.0, + "content": "entities, we randomly select a question template to generate a question given the subject; the object", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 318, + 506, + 332 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 506, + 332 + ], + "score": 1.0, + "content": "entity becomes the answer of the question. See Table 6 for the list of composed relations, sample", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 330, + 505, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 505, + 343 + ], + "score": 1.0, + "content": "questions, and answers. Note that all atomic relations in this dataset are many-to-one while these", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 341, + 372, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 341, + 372, + 353 + ], + "score": 1.0, + "content": "composed relations can be one-to-many or many-to-many as well.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 107, + 365, + 505, + 431 + ], + "lines": [ + { + "bbox": [ + 106, + 365, + 506, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 365, + 506, + 378 + ], + "score": 1.0, + "content": "Conjunctive queries. To generate question-and-answer pairs of conjunctive queries, we first", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 376, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 474, + 388 + ], + "score": 1.0, + "content": "picked three pairs of relations and used them to create query templates of the form “Find", + "type": "text" + }, + { + "bbox": [ + 474, + 376, + 501, + 387 + ], + "score": 0.89, + "content": "e \\in { \\mathcal { E } }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 376, + 505, + 388 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 385, + 506, + 400 + ], + "spans": [ + { + "bbox": [ + 104, + 385, + 165, + 400 + ], + "score": 1.0, + "content": "such that both", + "type": "text" + }, + { + "bbox": [ + 165, + 387, + 205, + 398 + ], + "score": 0.92, + "content": "( s _ { 1 } , r _ { 1 } , e )", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 385, + 223, + 400 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 224, + 387, + 263, + 399 + ], + "score": 0.92, + "content": "( s _ { 2 } , r _ { 2 } , e )", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 385, + 448, + 400 + ], + "score": 1.0, + "content": "are true.” (see Table 5). For a pair of relations", + "type": "text" + }, + { + "bbox": [ + 449, + 388, + 459, + 398 + ], + "score": 0.85, + "content": "r _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 385, + 477, + 400 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 477, + 388, + 487, + 398 + ], + "score": 0.85, + "content": "r _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 385, + 506, + 400 + ], + "score": 1.0, + "content": ", we", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 104, + 396, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 104, + 396, + 235, + 411 + ], + "score": 1.0, + "content": "enumerated all pairs of entities", + "type": "text" + }, + { + "bbox": [ + 235, + 400, + 260, + 409 + ], + "score": 0.42, + "content": "s _ { 1 } , s _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 261, + 396, + 506, + 411 + ], + "score": 1.0, + "content": "that can be their subjects and formulated the corresponding", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "score": 1.0, + "content": "query in natural language using question templates as in the same way as path queries. See Table 7", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 420, + 278, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 278, + 432 + ], + "score": 1.0, + "content": "for a list of sample questions and answers.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28.5 + }, + { + "type": "text", + "bbox": [ + 107, + 437, + 505, + 470 + ], + "lines": [ + { + "bbox": [ + 105, + 437, + 505, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 505, + 449 + ], + "score": 1.0, + "content": "As a result, we created 8003 question-and-answer pairs of path queries and 2208 pairs of conjunctive", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 447, + 506, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 319, + 460 + ], + "score": 1.0, + "content": "queries which are partitioned into train / validation", + "type": "text" + }, + { + "bbox": [ + 320, + 448, + 325, + 457 + ], + "score": 0.33, + "content": "/", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 447, + 506, + 460 + ], + "score": 1.0, + "content": "test subsets. We refer to Table 1 for more", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 459, + 447, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 447, + 471 + ], + "score": 1.0, + "content": "statistics about the dataset. Templates for generating the questions are list in Table 5.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33 + }, + { + "type": "title", + "bbox": [ + 108, + 484, + 228, + 495 + ], + "lines": [ + { + "bbox": [ + 106, + 483, + 230, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 483, + 230, + 496 + ], + "score": 1.0, + "content": "4.2 EXPERIMENTAL SETUP", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 504, + 505, + 603 + ], + "lines": [ + { + "bbox": [ + 106, + 505, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 505, + 516 + ], + "score": 1.0, + "content": "To perform question and answering under our proposed framework, we first train the TransGaussian", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 515, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 505, + 527 + ], + "score": 1.0, + "content": "model on WorldCup2014 dataset. In addition to the atomic triplets, we randomly sampled 50000", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 526, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 526, + 505, + 539 + ], + "score": 1.0, + "content": "paths with length 1 or 2 from the knowledge graph and trained a TransGaussian model composi-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 104, + 535, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 104, + 535, + 505, + 551 + ], + "score": 1.0, + "content": "tionally as described in Set 2.2. An inverse relation is treated as a separate relation. Following", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 549, + 504, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 504, + 560 + ], + "score": 1.0, + "content": "the naming convention from Guu et al. (2015), we denote this trained embedding by TransGaus-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 558, + 505, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 505, + 572 + ], + "score": 1.0, + "content": "sian (COMP). We found that the learned embedding possess some interesting properties. Some", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 569, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 505, + 583 + ], + "score": 1.0, + "content": "dimensions of the embedding space dedicate to represent a particular relation. Players are clustered", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 580, + 506, + 594 + ], + "spans": [ + { + "bbox": [ + 105, + 580, + 506, + 594 + ], + "score": 1.0, + "content": "by their attributes when entities’ embeddings are projected to the corresponding lower dimensional", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 592, + 393, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 393, + 605 + ], + "score": 1.0, + "content": "subspaces. We elaborate and illustrate such properties in the Appendix.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 107, + 615, + 504, + 671 + ], + "lines": [ + { + "bbox": [ + 106, + 616, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 505, + 628 + ], + "score": 1.0, + "content": "Baseline methods We also trained a TransGaussian model only on the atomic triplets and denote", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 627, + 505, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 627, + 505, + 639 + ], + "score": 1.0, + "content": "such a model by TransGaussian (SINGLE). Since no inverse relation was involved when Trans-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 637, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 506, + 651 + ], + "score": 1.0, + "content": "Gaussian (SINGLE) was trained, to use this embedding in question answering tasks, we represent", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 649, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 309, + 661 + ], + "score": 1.0, + "content": "the inverse relations as follows: for each relation", + "type": "text" + }, + { + "bbox": [ + 310, + 651, + 316, + 659 + ], + "score": 0.68, + "content": "r", + "type": "inline_equation" + }, + { + "bbox": [ + 316, + 649, + 363, + 661 + ], + "score": 1.0, + "content": "with mean", + "type": "text" + }, + { + "bbox": [ + 364, + 649, + 375, + 660 + ], + "score": 0.88, + "content": "\\delta _ { r }", + "type": "inline_equation" + }, + { + "bbox": [ + 375, + 649, + 431, + 661 + ], + "score": 1.0, + "content": "and variance", + "type": "text" + }, + { + "bbox": [ + 432, + 649, + 445, + 660 + ], + "score": 0.88, + "content": "\\Sigma _ { r }", + "type": "inline_equation" + }, + { + "bbox": [ + 445, + 649, + 505, + 661 + ], + "score": 1.0, + "content": ", we model its", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 659, + 418, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 137, + 672 + ], + "score": 1.0, + "content": "inverse", + "type": "text" + }, + { + "bbox": [ + 137, + 659, + 154, + 670 + ], + "score": 0.9, + "content": "r ^ { - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 154, + 659, + 293, + 672 + ], + "score": 1.0, + "content": "as a Gaussian attention with mean", + "type": "text" + }, + { + "bbox": [ + 294, + 660, + 312, + 671 + ], + "score": 0.89, + "content": "- \\delta _ { r }", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 659, + 401, + 672 + ], + "score": 1.0, + "content": "and variance equal to", + "type": "text" + }, + { + "bbox": [ + 401, + 660, + 415, + 671 + ], + "score": 0.89, + "content": "\\Sigma _ { r }", + "type": "inline_equation" + }, + { + "bbox": [ + 415, + 659, + 418, + 672 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 47 + }, + { + "type": "text", + "bbox": [ + 107, + 676, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "We also trained TransE models on WorldCup2014 dataset by using the code released by the authors", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "of Guu et al. (2015). Likewise, we use TransE (SINGLE) to denote the model trained with atomic", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "score": 1.0, + "content": "triplets only and use TransE (COMP) to denote the model trained with the union of triplets and", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "score": 1.0, + "content": "paths. Note that TransE can be considered as a special case of TransGaussian where the variance", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 105, + 720, + 474, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 474, + 732 + ], + "score": 1.0, + "content": "matrix is the identity and hence, the scoring formula Eq. (7) is applicable to TransE as well.", + "type": "text" + } + ], + "index": 54 + } + ], + "index": 52 + } + ], + "page_idx": 6, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 107, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 107, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 303, + 751, + 309, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "score": 1.0, + "content": "7", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 111, + 80, + 318, + 114 + ], + "lines": [], + "index": 2, + "bbox_fs": [ + 111, + 80, + 319, + 115 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 329, + 81, + 519, + 114 + ], + "lines": [], + "index": 3, + "bbox_fs": [ + 329, + 80, + 521, + 115 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 108, + 114, + 506, + 147 + ], + "lines": [ + { + "bbox": [ + 106, + 113, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 106, + 113, + 506, + 127 + ], + "score": 1.0, + "content": "where PLAYER, CLUB, NUMBER, etc, denote the type of entities that can appear as the left or", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 124, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 124, + 506, + 139 + ], + "score": 1.0, + "content": "right argument for each relation. Some relations share the same type as the right argument, e.g.,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 136, + 302, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 136, + 302, + 149 + ], + "score": 1.0, + "content": "plays for country and is in country.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7, + "bbox_fs": [ + 105, + 113, + 506, + 149 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 153, + 505, + 208 + ], + "lines": [ + { + "bbox": [ + 106, + 152, + 505, + 164 + ], + "spans": [ + { + "bbox": [ + 106, + 152, + 505, + 164 + ], + "score": 1.0, + "content": "Given the entities and relations, we transformed the dataset into a set of 3977 triplets. A list of", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 163, + 505, + 176 + ], + "spans": [ + { + "bbox": [ + 105, + 163, + 505, + 176 + ], + "score": 1.0, + "content": "sample triplets can be found in the Appendix. Based on these triplets, we created two sets of question", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 174, + 505, + 188 + ], + "spans": [ + { + "bbox": [ + 105, + 174, + 505, + 188 + ], + "score": 1.0, + "content": "answering tasks which we call path query and conjunctive query respectively. The answer of every", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 185, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 505, + 200 + ], + "score": 1.0, + "content": "question is always an entity in the knowledge base and a question can involve one or two triplets.", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 196, + 266, + 210 + ], + "spans": [ + { + "bbox": [ + 106, + 196, + 266, + 210 + ], + "score": 1.0, + "content": "The questions are generated as follows.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11, + "bbox_fs": [ + 105, + 152, + 505, + 210 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 221, + 505, + 352 + ], + "lines": [ + { + "bbox": [ + 104, + 219, + 506, + 233 + ], + "spans": [ + { + "bbox": [ + 104, + 219, + 506, + 233 + ], + "score": 1.0, + "content": "Path queries. Among the paths on the knowledge graph, there are some natural composition of", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 232, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 232, + 304, + 244 + ], + "score": 1.0, + "content": "relations, e.g., plays in country (PLAYER", + "type": "text" + }, + { + "bbox": [ + 304, + 232, + 318, + 242 + ], + "score": 0.78, + "content": "", + "type": "inline_equation" + }, + { + "bbox": [ + 319, + 232, + 505, + 244 + ], + "score": 1.0, + "content": "COUNTRY) can be decomposed as the com-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 242, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 261, + 255 + ], + "score": 1.0, + "content": "position of plays in club (PLAYE", + "type": "text" + }, + { + "bbox": [ + 262, + 243, + 296, + 253 + ], + "score": 0.34, + "content": "\\mathbf { R } \\to \\mathbf { C L } ", + "type": "inline_equation" + }, + { + "bbox": [ + 297, + 242, + 406, + 255 + ], + "score": 1.0, + "content": "UB) and is in country", + "type": "text" + }, + { + "bbox": [ + 406, + 243, + 501, + 253 + ], + "score": 0.59, + "content": "( \\mathbf { C L U B } \\to \\mathbf { C O U N T R Y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 242, + 505, + 255 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 254, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 505, + 266 + ], + "score": 1.0, + "content": "In addition to the atomic relations, we manually picked a few meaningful compositions of relations", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 264, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 334, + 277 + ], + "score": 1.0, + "content": "and formed query templates, which takes the form “find", + "type": "text" + }, + { + "bbox": [ + 334, + 264, + 360, + 275 + ], + "score": 0.9, + "content": "e \\in { \\mathcal { E } }", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 264, + 403, + 277 + ], + "score": 1.0, + "content": ", such that", + "type": "text" + }, + { + "bbox": [ + 403, + 264, + 434, + 276 + ], + "score": 0.93, + "content": "( s , p , e )", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 264, + 497, + 277 + ], + "score": 1.0, + "content": "is true”, where", + "type": "text" + }, + { + "bbox": [ + 498, + 266, + 504, + 274 + ], + "score": 0.48, + "content": "s", + "type": "inline_equation" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 275, + 505, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 177, + 287 + ], + "score": 1.0, + "content": "is the subject and", + "type": "text" + }, + { + "bbox": [ + 177, + 277, + 184, + 287 + ], + "score": 0.8, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 185, + 275, + 505, + 287 + ], + "score": 1.0, + "content": "can be an atomic relation or a path of relations. To formulate a set of path-based", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 287, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 505, + 299 + ], + "score": 1.0, + "content": "question-answer pairs, we manually created one or more question templates for every query tem-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 297, + 506, + 310 + ], + "spans": [ + { + "bbox": [ + 104, + 297, + 506, + 310 + ], + "score": 1.0, + "content": "plate (see Table 5) Then, for a particular instantiation of a query template with subject and object", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 308, + 506, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 506, + 322 + ], + "score": 1.0, + "content": "entities, we randomly select a question template to generate a question given the subject; the object", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 318, + 506, + 332 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 506, + 332 + ], + "score": 1.0, + "content": "entity becomes the answer of the question. See Table 6 for the list of composed relations, sample", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 330, + 505, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 505, + 343 + ], + "score": 1.0, + "content": "questions, and answers. Note that all atomic relations in this dataset are many-to-one while these", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 341, + 372, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 341, + 372, + 353 + ], + "score": 1.0, + "content": "composed relations can be one-to-many or many-to-many as well.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 19.5, + "bbox_fs": [ + 104, + 219, + 506, + 353 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 365, + 505, + 431 + ], + "lines": [ + { + "bbox": [ + 106, + 365, + 506, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 365, + 506, + 378 + ], + "score": 1.0, + "content": "Conjunctive queries. To generate question-and-answer pairs of conjunctive queries, we first", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 376, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 474, + 388 + ], + "score": 1.0, + "content": "picked three pairs of relations and used them to create query templates of the form “Find", + "type": "text" + }, + { + "bbox": [ + 474, + 376, + 501, + 387 + ], + "score": 0.89, + "content": "e \\in { \\mathcal { E } }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 376, + 505, + 388 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 385, + 506, + 400 + ], + "spans": [ + { + "bbox": [ + 104, + 385, + 165, + 400 + ], + "score": 1.0, + "content": "such that both", + "type": "text" + }, + { + "bbox": [ + 165, + 387, + 205, + 398 + ], + "score": 0.92, + "content": "( s _ { 1 } , r _ { 1 } , e )", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 385, + 223, + 400 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 224, + 387, + 263, + 399 + ], + "score": 0.92, + "content": "( s _ { 2 } , r _ { 2 } , e )", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 385, + 448, + 400 + ], + "score": 1.0, + "content": "are true.” (see Table 5). For a pair of relations", + "type": "text" + }, + { + "bbox": [ + 449, + 388, + 459, + 398 + ], + "score": 0.85, + "content": "r _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 385, + 477, + 400 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 477, + 388, + 487, + 398 + ], + "score": 0.85, + "content": "r _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 385, + 506, + 400 + ], + "score": 1.0, + "content": ", we", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 104, + 396, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 104, + 396, + 235, + 411 + ], + "score": 1.0, + "content": "enumerated all pairs of entities", + "type": "text" + }, + { + "bbox": [ + 235, + 400, + 260, + 409 + ], + "score": 0.42, + "content": "s _ { 1 } , s _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 261, + 396, + 506, + 411 + ], + "score": 1.0, + "content": "that can be their subjects and formulated the corresponding", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "score": 1.0, + "content": "query in natural language using question templates as in the same way as path queries. See Table 7", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 420, + 278, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 278, + 432 + ], + "score": 1.0, + "content": "for a list of sample questions and answers.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28.5, + "bbox_fs": [ + 104, + 365, + 506, + 432 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 437, + 505, + 470 + ], + "lines": [ + { + "bbox": [ + 105, + 437, + 505, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 505, + 449 + ], + "score": 1.0, + "content": "As a result, we created 8003 question-and-answer pairs of path queries and 2208 pairs of conjunctive", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 447, + 506, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 319, + 460 + ], + "score": 1.0, + "content": "queries which are partitioned into train / validation", + "type": "text" + }, + { + "bbox": [ + 320, + 448, + 325, + 457 + ], + "score": 0.33, + "content": "/", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 447, + 506, + 460 + ], + "score": 1.0, + "content": "test subsets. We refer to Table 1 for more", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 459, + 447, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 447, + 471 + ], + "score": 1.0, + "content": "statistics about the dataset. Templates for generating the questions are list in Table 5.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33, + "bbox_fs": [ + 105, + 437, + 506, + 471 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 484, + 228, + 495 + ], + "lines": [ + { + "bbox": [ + 106, + 483, + 230, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 483, + 230, + 496 + ], + "score": 1.0, + "content": "4.2 EXPERIMENTAL SETUP", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 504, + 505, + 603 + ], + "lines": [ + { + "bbox": [ + 106, + 505, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 505, + 516 + ], + "score": 1.0, + "content": "To perform question and answering under our proposed framework, we first train the TransGaussian", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 515, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 505, + 527 + ], + "score": 1.0, + "content": "model on WorldCup2014 dataset. In addition to the atomic triplets, we randomly sampled 50000", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 526, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 526, + 505, + 539 + ], + "score": 1.0, + "content": "paths with length 1 or 2 from the knowledge graph and trained a TransGaussian model composi-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 104, + 535, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 104, + 535, + 505, + 551 + ], + "score": 1.0, + "content": "tionally as described in Set 2.2. An inverse relation is treated as a separate relation. Following", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 549, + 504, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 504, + 560 + ], + "score": 1.0, + "content": "the naming convention from Guu et al. (2015), we denote this trained embedding by TransGaus-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 558, + 505, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 505, + 572 + ], + "score": 1.0, + "content": "sian (COMP). We found that the learned embedding possess some interesting properties. Some", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 569, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 505, + 583 + ], + "score": 1.0, + "content": "dimensions of the embedding space dedicate to represent a particular relation. Players are clustered", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 580, + 506, + 594 + ], + "spans": [ + { + "bbox": [ + 105, + 580, + 506, + 594 + ], + "score": 1.0, + "content": "by their attributes when entities’ embeddings are projected to the corresponding lower dimensional", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 592, + 393, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 393, + 605 + ], + "score": 1.0, + "content": "subspaces. We elaborate and illustrate such properties in the Appendix.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 40, + "bbox_fs": [ + 104, + 505, + 506, + 605 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 615, + 504, + 671 + ], + "lines": [ + { + "bbox": [ + 106, + 616, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 505, + 628 + ], + "score": 1.0, + "content": "Baseline methods We also trained a TransGaussian model only on the atomic triplets and denote", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 627, + 505, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 627, + 505, + 639 + ], + "score": 1.0, + "content": "such a model by TransGaussian (SINGLE). Since no inverse relation was involved when Trans-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 637, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 506, + 651 + ], + "score": 1.0, + "content": "Gaussian (SINGLE) was trained, to use this embedding in question answering tasks, we represent", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 649, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 309, + 661 + ], + "score": 1.0, + "content": "the inverse relations as follows: for each relation", + "type": "text" + }, + { + "bbox": [ + 310, + 651, + 316, + 659 + ], + "score": 0.68, + "content": "r", + "type": "inline_equation" + }, + { + "bbox": [ + 316, + 649, + 363, + 661 + ], + "score": 1.0, + "content": "with mean", + "type": "text" + }, + { + "bbox": [ + 364, + 649, + 375, + 660 + ], + "score": 0.88, + "content": "\\delta _ { r }", + "type": "inline_equation" + }, + { + "bbox": [ + 375, + 649, + 431, + 661 + ], + "score": 1.0, + "content": "and variance", + "type": "text" + }, + { + "bbox": [ + 432, + 649, + 445, + 660 + ], + "score": 0.88, + "content": "\\Sigma _ { r }", + "type": "inline_equation" + }, + { + "bbox": [ + 445, + 649, + 505, + 661 + ], + "score": 1.0, + "content": ", we model its", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 659, + 418, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 137, + 672 + ], + "score": 1.0, + "content": "inverse", + "type": "text" + }, + { + "bbox": [ + 137, + 659, + 154, + 670 + ], + "score": 0.9, + "content": "r ^ { - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 154, + 659, + 293, + 672 + ], + "score": 1.0, + "content": "as a Gaussian attention with mean", + "type": "text" + }, + { + "bbox": [ + 294, + 660, + 312, + 671 + ], + "score": 0.89, + "content": "- \\delta _ { r }", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 659, + 401, + 672 + ], + "score": 1.0, + "content": "and variance equal to", + "type": "text" + }, + { + "bbox": [ + 401, + 660, + 415, + 671 + ], + "score": 0.89, + "content": "\\Sigma _ { r }", + "type": "inline_equation" + }, + { + "bbox": [ + 415, + 659, + 418, + 672 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 47, + "bbox_fs": [ + 105, + 616, + 506, + 672 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 676, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "We also trained TransE models on WorldCup2014 dataset by using the code released by the authors", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "of Guu et al. (2015). Likewise, we use TransE (SINGLE) to denote the model trained with atomic", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "score": 1.0, + "content": "triplets only and use TransE (COMP) to denote the model trained with the union of triplets and", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "score": 1.0, + "content": "paths. Note that TransE can be considered as a special case of TransGaussian where the variance", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 105, + 720, + 474, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 474, + 732 + ], + "score": 1.0, + "content": "matrix is the identity and hence, the scoring formula Eq. (7) is applicable to TransE as well.", + "type": "text" + } + ], + "index": 54 + } + ], + "index": 52, + "bbox_fs": [ + 105, + 676, + 506, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 159 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "Training configurations For all models, dimension of entity embeddings was set to 30. The hid-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 91, + 505, + 108 + ], + "spans": [ + { + "bbox": [ + 105, + 91, + 505, + 108 + ], + "score": 1.0, + "content": "den size of LSTM was set to 80. Word embeddings were trained jointly with the question answering", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 505, + 116 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 505, + 116 + ], + "score": 1.0, + "content": "model and dimension of word embedding was set to 40. We employed Adam (Kingma & Ba, 2014)", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 114, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 114, + 506, + 129 + ], + "score": 1.0, + "content": "as the optimizer. All parameters were tuned on the validation set. Under the same setting, we exper-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "score": 1.0, + "content": "imented with two cases: first, we trained models for path queries and conjunctive queries separately;", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "score": 1.0, + "content": "Furthermore, we trained a single model that addresses both types queries. We present the results of", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 496, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 496, + 161 + ], + "score": 1.0, + "content": "the latter case in the next subsection while the results of the former are included in the Appendix.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 107, + 171, + 505, + 260 + ], + "lines": [ + { + "bbox": [ + 106, + 172, + 506, + 184 + ], + "spans": [ + { + "bbox": [ + 106, + 172, + 506, + 184 + ], + "score": 1.0, + "content": "Evaluation metrics During test time, our model receives a question in natural language and a list", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 183, + 506, + 195 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 506, + 195 + ], + "score": 1.0, + "content": "of knowledge base entities contained in the question. Then it predicts the mean and variance of a", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 194, + 505, + 206 + ], + "spans": [ + { + "bbox": [ + 106, + 194, + 505, + 206 + ], + "score": 1.0, + "content": "Gaussian attention formulated in Eq. (7) which is expected to capture the distribution of all positive", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 205, + 504, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 205, + 504, + 216 + ], + "score": 1.0, + "content": "answers. We rank all entities in the knowledge base by their scores under this Gaussian attention.", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 216, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 106, + 216, + 505, + 228 + ], + "score": 1.0, + "content": "Next, for each entity which is a correct answer, we check its rank relative to all incorrect answers and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 227, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 505, + 239 + ], + "score": 1.0, + "content": "call this rank the filtered rank. For example, if a correct entity is ranked above all negative answers", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 237, + 505, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 505, + 250 + ], + "score": 1.0, + "content": "except for one, it has filtered rank two. We compute this rank for all true answers and report mean", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 249, + 458, + 261 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 174, + 261 + ], + "score": 1.0, + "content": "filtered rank and", + "type": "text" + }, + { + "bbox": [ + 174, + 249, + 197, + 259 + ], + "score": 0.71, + "content": "H @ l", + "type": "inline_equation" + }, + { + "bbox": [ + 198, + 249, + 458, + 261 + ], + "score": 1.0, + "content": "which is the percentage of true answers that have filtered rank 1.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 10.5 + }, + { + "type": "title", + "bbox": [ + 108, + 273, + 239, + 284 + ], + "lines": [ + { + "bbox": [ + 105, + 272, + 240, + 286 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 240, + 286 + ], + "score": 1.0, + "content": "4.3 EXPERIMENTAL RESULTS", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 293, + 505, + 349 + ], + "lines": [ + { + "bbox": [ + 106, + 294, + 505, + 306 + ], + "spans": [ + { + "bbox": [ + 106, + 294, + 505, + 306 + ], + "score": 1.0, + "content": "We present the results of joint learning in Table 2. These results show that TransGaussian works", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 304, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 505, + 317 + ], + "score": 1.0, + "content": "better than TransE in general. In fact, TransGaussian (COMP) achieved the best performance in", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 315, + 506, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 335, + 329 + ], + "score": 1.0, + "content": "almost all aspects. Most notably, it achieved the highest", + "type": "text" + }, + { + "bbox": [ + 335, + 316, + 358, + 326 + ], + "score": 0.81, + "content": "\\mathrm { H @ 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 359, + 315, + 506, + 329 + ], + "score": 1.0, + "content": "rates on challenging questions such", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 326, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 505, + 339 + ], + "score": 1.0, + "content": "as “where is the club that edin dzeko plays for?” (#11, composition of two relations) and “who are", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 338, + 411, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 411, + 351 + ], + "score": 1.0, + "content": "the defenders on german national team?” (#14, conjunction of two queries).", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 354, + 505, + 398 + ], + "lines": [ + { + "bbox": [ + 105, + 354, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 505, + 367 + ], + "score": 1.0, + "content": "The same table shows that TransGaussian benefits remarkably from compositional training. For", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 366, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 350, + 378 + ], + "score": 1.0, + "content": "example, compositional training improved TransGaussian’s", + "type": "text" + }, + { + "bbox": [ + 350, + 366, + 373, + 376 + ], + "score": 0.78, + "content": "\\mathrm { H @ 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 374, + 366, + 427, + 378 + ], + "score": 1.0, + "content": "rate by near", + "type": "text" + }, + { + "bbox": [ + 427, + 366, + 447, + 376 + ], + "score": 0.86, + "content": "60 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 366, + 505, + 378 + ], + "score": 1.0, + "content": "in queries on", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 377, + 506, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 506, + 390 + ], + "score": 1.0, + "content": "players from a given countries (#8) and queries on players who play a particular position (#9). It", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 387, + 477, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 477, + 400 + ], + "score": 1.0, + "content": "also boosted TransGaussian’s performance on all conjunctive quries (#13–#15) significantly.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 107, + 404, + 505, + 482 + ], + "lines": [ + { + "bbox": [ + 105, + 403, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 505, + 417 + ], + "score": 1.0, + "content": "To understand TransGaussian (COMP)’s weak performance on answering queries on the profes-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 415, + 506, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 506, + 429 + ], + "score": 1.0, + "content": "sional football club located in a given country (#10) and queries on professional football club that", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 426, + 505, + 439 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 505, + 439 + ], + "score": 1.0, + "content": "has players from a particular country (#12), we tested its capability of modeling the composed re-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 438, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 505, + 450 + ], + "score": 1.0, + "content": "lation by feeding the correct relations and subjects during test time. It turns out that these two", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 448, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 505, + 461 + ], + "score": 1.0, + "content": "relations were not modeled well by TransGaussian (COMP) embedding, which limits its perfor-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 460, + 505, + 472 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 505, + 472 + ], + "score": 1.0, + "content": "mance in question answering. (See Table 8 in the Appendix for quantitative evaluations.) The same", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 470, + 325, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 325, + 483 + ], + "score": 1.0, + "content": "limit was found in the other three embeddings as well.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 487, + 505, + 543 + ], + "lines": [ + { + "bbox": [ + 105, + 487, + 506, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 487, + 506, + 500 + ], + "score": 1.0, + "content": "Note that all the models compared in Table 2 uses the proposed Gaussian attention model because", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 498, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 498, + 505, + 509 + ], + "score": 1.0, + "content": "TransE is the special case of TransGaussian where the variance is fixed to one. Thus the main differ-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 508, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 505, + 522 + ], + "score": 1.0, + "content": "ences are whether the variance is learned and whether the embedding was trained compositionally.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 519, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 505, + 533 + ], + "score": 1.0, + "content": "Finally, we refer to Table 9 and 10 in the Appendix for experimental results of models trained on", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 531, + 267, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 267, + 545 + ], + "score": 1.0, + "content": "path and conjunctive queries separately.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34 + }, + { + "type": "table", + "bbox": [ + 107, + 572, + 535, + 609 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 196, + 552, + 414, + 564 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 195, + 550, + 415, + 566 + ], + "spans": [ + { + "bbox": [ + 195, + 550, + 415, + 566 + ], + "score": 1.0, + "content": "Table 1: Some statistics of the WorldCup2014 dataset.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37 + }, + { + "type": "table_body", + "bbox": [ + 107, + 572, + 535, + 609 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 572, + 535, + 609 + ], + "spans": [ + { + "bbox": [ + 107, + 572, + 535, + 609 + ], + "score": 0.962, + "html": "
# entity
#atomic relations# atomic triplets
# path query Q&A（train/validation/test）# conjunctive query Q&A（train /validation /test）
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", + "type": "table", + "image_path": "aad02463c0fedf6a70824602adf903d1fff0827b0c92885dcdc8d3417dc51591.jpg" + } + ] + } + ], + "index": 39, + "virtual_lines": [ + { + "bbox": [ + 107, + 572, + 535, + 584.3333333333334 + ], + "spans": [], + "index": 38 + }, + { + "bbox": [ + 107, + 584.3333333333334, + 535, + 596.6666666666667 + ], + "spans": [], + "index": 39 + }, + { + "bbox": [ + 107, + 596.6666666666667, + 535, + 609.0000000000001 + ], + "spans": [], + "index": 40 + } + ] + } + ], + "index": 38.0 + }, + { + "type": "title", + "bbox": [ + 108, + 630, + 209, + 642 + ], + "lines": [ + { + "bbox": [ + 105, + 628, + 211, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 211, + 644 + ], + "score": 1.0, + "content": "5 RELATED WORK", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 106, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "The work of Vilnis & McCallum (2014) is similar to our Gaussian attention model. They discuss", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 665, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 679 + ], + "score": 1.0, + "content": "many advantages of the Gaussian embedding; for example, it is arguably a better way of handling", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "asymmetric relations and entailment. However the work was presented in the word2vec (Mikolov", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 689, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 504, + 700 + ], + "score": 1.0, + "content": "et al., 2013)-style word embedding setting and the Gaussian embedding was used to capture the", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "diversity in the meaning of a word. Our Gaussian attention model extends their work to a more", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 710, + 507, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 507, + 723 + ], + "score": 1.0, + "content": "general setting in which any memory item can be addressed through a concept represented as a", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 720, + 290, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 290, + 733 + ], + "score": 1.0, + "content": "Gaussian distribution over the memory items.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 45 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 107, + 25, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 107, + 25, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "score": 1.0, + "content": "8", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 159 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "Training configurations For all models, dimension of entity embeddings was set to 30. The hid-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 91, + 505, + 108 + ], + "spans": [ + { + "bbox": [ + 105, + 91, + 505, + 108 + ], + "score": 1.0, + "content": "den size of LSTM was set to 80. Word embeddings were trained jointly with the question answering", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 505, + 116 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 505, + 116 + ], + "score": 1.0, + "content": "model and dimension of word embedding was set to 40. We employed Adam (Kingma & Ba, 2014)", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 114, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 114, + 506, + 129 + ], + "score": 1.0, + "content": "as the optimizer. All parameters were tuned on the validation set. Under the same setting, we exper-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "score": 1.0, + "content": "imented with two cases: first, we trained models for path queries and conjunctive queries separately;", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "score": 1.0, + "content": "Furthermore, we trained a single model that addresses both types queries. We present the results of", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 496, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 496, + 161 + ], + "score": 1.0, + "content": "the latter case in the next subsection while the results of the former are included in the Appendix.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3, + "bbox_fs": [ + 105, + 82, + 506, + 161 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 171, + 505, + 260 + ], + "lines": [ + { + "bbox": [ + 106, + 172, + 506, + 184 + ], + "spans": [ + { + "bbox": [ + 106, + 172, + 506, + 184 + ], + "score": 1.0, + "content": "Evaluation metrics During test time, our model receives a question in natural language and a list", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 183, + 506, + 195 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 506, + 195 + ], + "score": 1.0, + "content": "of knowledge base entities contained in the question. Then it predicts the mean and variance of a", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 194, + 505, + 206 + ], + "spans": [ + { + "bbox": [ + 106, + 194, + 505, + 206 + ], + "score": 1.0, + "content": "Gaussian attention formulated in Eq. (7) which is expected to capture the distribution of all positive", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 205, + 504, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 205, + 504, + 216 + ], + "score": 1.0, + "content": "answers. We rank all entities in the knowledge base by their scores under this Gaussian attention.", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 216, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 106, + 216, + 505, + 228 + ], + "score": 1.0, + "content": "Next, for each entity which is a correct answer, we check its rank relative to all incorrect answers and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 227, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 505, + 239 + ], + "score": 1.0, + "content": "call this rank the filtered rank. For example, if a correct entity is ranked above all negative answers", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 237, + 505, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 505, + 250 + ], + "score": 1.0, + "content": "except for one, it has filtered rank two. We compute this rank for all true answers and report mean", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 249, + 458, + 261 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 174, + 261 + ], + "score": 1.0, + "content": "filtered rank and", + "type": "text" + }, + { + "bbox": [ + 174, + 249, + 197, + 259 + ], + "score": 0.71, + "content": "H @ l", + "type": "inline_equation" + }, + { + "bbox": [ + 198, + 249, + 458, + 261 + ], + "score": 1.0, + "content": "which is the percentage of true answers that have filtered rank 1.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 10.5, + "bbox_fs": [ + 105, + 172, + 506, + 261 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 273, + 239, + 284 + ], + "lines": [ + { + "bbox": [ + 105, + 272, + 240, + 286 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 240, + 286 + ], + "score": 1.0, + "content": "4.3 EXPERIMENTAL RESULTS", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 293, + 505, + 349 + ], + "lines": [ + { + "bbox": [ + 106, + 294, + 505, + 306 + ], + "spans": [ + { + "bbox": [ + 106, + 294, + 505, + 306 + ], + "score": 1.0, + "content": "We present the results of joint learning in Table 2. These results show that TransGaussian works", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 304, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 505, + 317 + ], + "score": 1.0, + "content": "better than TransE in general. In fact, TransGaussian (COMP) achieved the best performance in", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 315, + 506, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 335, + 329 + ], + "score": 1.0, + "content": "almost all aspects. Most notably, it achieved the highest", + "type": "text" + }, + { + "bbox": [ + 335, + 316, + 358, + 326 + ], + "score": 0.81, + "content": "\\mathrm { H @ 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 359, + 315, + 506, + 329 + ], + "score": 1.0, + "content": "rates on challenging questions such", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 326, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 505, + 339 + ], + "score": 1.0, + "content": "as “where is the club that edin dzeko plays for?” (#11, composition of two relations) and “who are", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 338, + 411, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 411, + 351 + ], + "score": 1.0, + "content": "the defenders on german national team?” (#14, conjunction of two queries).", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 294, + 506, + 351 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 354, + 505, + 398 + ], + "lines": [ + { + "bbox": [ + 105, + 354, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 505, + 367 + ], + "score": 1.0, + "content": "The same table shows that TransGaussian benefits remarkably from compositional training. For", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 366, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 350, + 378 + ], + "score": 1.0, + "content": "example, compositional training improved TransGaussian’s", + "type": "text" + }, + { + "bbox": [ + 350, + 366, + 373, + 376 + ], + "score": 0.78, + "content": "\\mathrm { H @ 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 374, + 366, + 427, + 378 + ], + "score": 1.0, + "content": "rate by near", + "type": "text" + }, + { + "bbox": [ + 427, + 366, + 447, + 376 + ], + "score": 0.86, + "content": "60 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 366, + 505, + 378 + ], + "score": 1.0, + "content": "in queries on", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 377, + 506, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 506, + 390 + ], + "score": 1.0, + "content": "players from a given countries (#8) and queries on players who play a particular position (#9). It", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 387, + 477, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 477, + 400 + ], + "score": 1.0, + "content": "also boosted TransGaussian’s performance on all conjunctive quries (#13–#15) significantly.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 354, + 506, + 400 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 404, + 505, + 482 + ], + "lines": [ + { + "bbox": [ + 105, + 403, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 505, + 417 + ], + "score": 1.0, + "content": "To understand TransGaussian (COMP)’s weak performance on answering queries on the profes-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 415, + 506, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 506, + 429 + ], + "score": 1.0, + "content": "sional football club located in a given country (#10) and queries on professional football club that", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 426, + 505, + 439 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 505, + 439 + ], + "score": 1.0, + "content": "has players from a particular country (#12), we tested its capability of modeling the composed re-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 438, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 505, + 450 + ], + "score": 1.0, + "content": "lation by feeding the correct relations and subjects during test time. It turns out that these two", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 448, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 505, + 461 + ], + "score": 1.0, + "content": "relations were not modeled well by TransGaussian (COMP) embedding, which limits its perfor-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 460, + 505, + 472 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 505, + 472 + ], + "score": 1.0, + "content": "mance in question answering. (See Table 8 in the Appendix for quantitative evaluations.) The same", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 470, + 325, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 325, + 483 + ], + "score": 1.0, + "content": "limit was found in the other three embeddings as well.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28, + "bbox_fs": [ + 105, + 403, + 506, + 483 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 487, + 505, + 543 + ], + "lines": [ + { + "bbox": [ + 105, + 487, + 506, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 487, + 506, + 500 + ], + "score": 1.0, + "content": "Note that all the models compared in Table 2 uses the proposed Gaussian attention model because", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 498, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 498, + 505, + 509 + ], + "score": 1.0, + "content": "TransE is the special case of TransGaussian where the variance is fixed to one. Thus the main differ-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 508, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 505, + 522 + ], + "score": 1.0, + "content": "ences are whether the variance is learned and whether the embedding was trained compositionally.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 519, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 505, + 533 + ], + "score": 1.0, + "content": "Finally, we refer to Table 9 and 10 in the Appendix for experimental results of models trained on", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 531, + 267, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 267, + 545 + ], + "score": 1.0, + "content": "path and conjunctive queries separately.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 487, + 506, + 545 + ] + }, + { + "type": "table", + "bbox": [ + 107, + 572, + 535, + 609 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 196, + 552, + 414, + 564 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 195, + 550, + 415, + 566 + ], + "spans": [ + { + "bbox": [ + 195, + 550, + 415, + 566 + ], + "score": 1.0, + "content": "Table 1: Some statistics of the WorldCup2014 dataset.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37 + }, + { + "type": "table_body", + "bbox": [ + 107, + 572, + 535, + 609 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 572, + 535, + 609 + ], + "spans": [ + { + "bbox": [ + 107, + 572, + 535, + 609 + ], + "score": 0.962, + "html": "
# entity
#atomic relations# atomic triplets
# path query Q&A（train/validation/test）# conjunctive query Q&A（train /validation /test）
1127639775620/804/15791564/224/420
", + "type": "table", + "image_path": "aad02463c0fedf6a70824602adf903d1fff0827b0c92885dcdc8d3417dc51591.jpg" + } + ] + } + ], + "index": 39, + "virtual_lines": [ + { + "bbox": [ + 107, + 572, + 535, + 584.3333333333334 + ], + "spans": [], + "index": 38 + }, + { + "bbox": [ + 107, + 584.3333333333334, + 535, + 596.6666666666667 + ], + "spans": [], + "index": 39 + }, + { + "bbox": [ + 107, + 596.6666666666667, + 535, + 609.0000000000001 + ], + "spans": [], + "index": 40 + } + ] + } + ], + "index": 38.0 + }, + { + "type": "title", + "bbox": [ + 108, + 630, + 209, + 642 + ], + "lines": [ + { + "bbox": [ + 105, + 628, + 211, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 211, + 644 + ], + "score": 1.0, + "content": "5 RELATED WORK", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 106, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "The work of Vilnis & McCallum (2014) is similar to our Gaussian attention model. They discuss", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 665, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 679 + ], + "score": 1.0, + "content": "many advantages of the Gaussian embedding; for example, it is arguably a better way of handling", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "asymmetric relations and entailment. However the work was presented in the word2vec (Mikolov", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 689, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 504, + 700 + ], + "score": 1.0, + "content": "et al., 2013)-style word embedding setting and the Gaussian embedding was used to capture the", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "diversity in the meaning of a word. Our Gaussian attention model extends their work to a more", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 710, + 507, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 507, + 723 + ], + "score": 1.0, + "content": "general setting in which any memory item can be addressed through a concept represented as a", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 720, + 290, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 290, + 733 + ], + "score": 1.0, + "content": "Gaussian distribution over the memory items.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 45, + "bbox_fs": [ + 105, + 655, + 507, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 100, + 511, + 264 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 110, + 80, + 493, + 92 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 112, + 78, + 495, + 94 + ], + "spans": [ + { + "bbox": [ + 112, + 78, + 495, + 94 + ], + "score": 1.0, + "content": "Table 2: Results of joint learning with path queries and conjunction queries on WorldCup2014.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 106, + 100, + 511, + 264 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 100, + 511, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 100, + 511, + 264 + ], + "score": 0.983, + "html": "
TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#Sample questionH@1(%）FilteredMean RankH@1(%）FilteredMean RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered Rank
1which club does alan pulido play for?88.591.1891.951.1196.641.0498.661.01
2what position does gonzalo higuain play?100.001.0098.111.0398.741.01100.001.00
3how old is samuel etoo?67.111.4490.791.1394.741.0897.371.04
4what is the jersey number of mario balotelli?45.001.8983.571.2297.141.0399.291.01
5which country is thomas mueller from ?94.401.0694.401.0696.801.0498.401.02
6which country is the soccer team fc porto based in ?98.481.0298.481.0293.941.0695.451.05
7who plays professionally at liverpool fc?95.121.1090.241.2098.371.0496.751.04
8which player is from iran?89.861.5176.812.0738.652.9699.521.00
9name a player who plays goalkeeper?98.961.0169.791.8242.715.52100.001.00
10which soccer club is based in mexico?22.0313.9430.518.846.7810.6616.9521.14
11where is the club that edin dzeko plays for ？52.633.8857.242.1047.372.2778.291.41
12name a soccer club that has a player from australia ?30.4312.0833.7011.4713.0411.6419.5717.57
Overall (Path Query)74.163.1177.392.5669.543.0285.943.52
13who plays forward for fc barcelona?97.551.0676.071.6693.251.2498.771.02
14who are the defenders on german national team?95.931.0669.922.3365.042.04100.001.00
15which player in ssc napoli is from argentina?88.811.1776.121.7688.811.3597.761.03
Overall(Conj. Query)94.291.0974.291.8983.571.5198.811.02
", + "type": "table", + "image_path": "7b655a2b41aad14dfeb2d35e01d31e0083bc112661b419140489d25d63616d5e.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 106, + 100, + 511, + 154.66666666666666 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 106, + 154.66666666666666, + 511, + 209.33333333333331 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 106, + 209.33333333333331, + 511, + 264.0 + ], + "spans": [], + "index": 3 + } + ] + } + ], + "index": 1.0 + }, + { + "type": "text", + "bbox": [ + 107, + 291, + 505, + 368 + ], + "lines": [ + { + "bbox": [ + 105, + 291, + 505, + 303 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 505, + 303 + ], + "score": 1.0, + "content": "Bordes et al. (2014; 2015) proposed a question-answering model that embeds both questions and", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 302, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 505, + 315 + ], + "score": 1.0, + "content": "their answers to a common continuous vector space. Their method in Bordes et al. (2015) can", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 313, + 505, + 325 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 325 + ], + "score": 1.0, + "content": "combine multiple knowledge bases and even generalize to a knowledge base that was not used", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 324, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 505, + 336 + ], + "score": 1.0, + "content": "during training. However their method is limited to the simple question answering setting in which", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 335, + 505, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 505, + 346 + ], + "score": 1.0, + "content": "the answer of each question associated with a triplet in the knowledge base. In contrast, our method", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 345, + 504, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 504, + 358 + ], + "score": 1.0, + "content": "can handle both composition of relations and conjunction of conditions, which are both naturally", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 357, + 313, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 313, + 369 + ], + "score": 1.0, + "content": "enabled by the proposed Gaussian attention model.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 374, + 505, + 506 + ], + "lines": [ + { + "bbox": [ + 105, + 374, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 505, + 386 + ], + "score": 1.0, + "content": "Neelakantan et al. (2015a) proposed a method that combines relations to deal with compositional", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 385, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 106, + 385, + 505, + 396 + ], + "score": 1.0, + "content": "relations for knowledge base completion. Their key technical contribution is to use recurrent neural", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 396, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 505, + 408 + ], + "score": 1.0, + "content": "networks (RNNs) to encode a chain of relations. When we restrict ourselves to path queries, question", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 407, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 419 + ], + "score": 1.0, + "content": "answering can be seen as a sequence transduction task (Graves, 2012; Sutskever et al., 2014) in", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 417, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 505, + 430 + ], + "score": 1.0, + "content": "which the input is text and the output is a series of relations. If we use RNNs as a decoder, our model", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 429, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 505, + 441 + ], + "score": 1.0, + "content": "would be able to handle non-commutative composition of relations, which the current weighted", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 440, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 106, + 440, + 505, + 451 + ], + "score": 1.0, + "content": "convolution cannot handle well. Another interesting connection to our work is that they take the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 451, + 506, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 506, + 463 + ], + "score": 1.0, + "content": "maximum of the inner-product scores (see also Weston et al., 2013; Neelakantan et al., 2015b),", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 461, + 506, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 506, + 474 + ], + "score": 1.0, + "content": "which are computed along multiple paths connecting a pair of entities. Representing a set as a", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "score": 1.0, + "content": "collection of vectors and taking the maximum over the inner-product scores is a natural way to", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 484, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 505, + 496 + ], + "score": 1.0, + "content": "represent a set of memory items. The Gaussian attention model we propose in this paper, however,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 494, + 333, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 333, + 507 + ], + "score": 1.0, + "content": "has the advantage of differentiability and composability.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 16.5 + }, + { + "type": "title", + "bbox": [ + 108, + 528, + 195, + 540 + ], + "lines": [ + { + "bbox": [ + 104, + 525, + 197, + 543 + ], + "spans": [ + { + "bbox": [ + 104, + 525, + 197, + 543 + ], + "score": 1.0, + "content": "6 CONCLUSION", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 107, + 556, + 505, + 667 + ], + "lines": [ + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "score": 1.0, + "content": "In this paper, we have proposed the Gaussian attention model which can be used in a variety of", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 568, + 505, + 580 + ], + "spans": [ + { + "bbox": [ + 105, + 568, + 505, + 580 + ], + "score": 1.0, + "content": "contexts where we can assume that the distance between the memory items in the latent space is", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 577, + 506, + 592 + ], + "spans": [ + { + "bbox": [ + 104, + 577, + 506, + 592 + ], + "score": 1.0, + "content": "compatible with some notion of semantics. We have shown that the proposed Gaussian scoring", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 590, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 590, + 505, + 603 + ], + "score": 1.0, + "content": "function can be used for knowledge base embedding achieving competitive accuracy. We have also", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 601, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 506, + 613 + ], + "score": 1.0, + "content": "shown that our embedding model can naturally propagate uncertainty when we compose relations", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 612, + 505, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 612, + 505, + 623 + ], + "score": 1.0, + "content": "together. Our embedding model also benefits from compositional training proposed by Guu et al.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 623, + 504, + 634 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 504, + 634 + ], + "score": 1.0, + "content": "(2015). Furthermore, we have demonstrated the power of the Gaussian attention model in a chal-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 633, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 505, + 646 + ], + "score": 1.0, + "content": "lenging question answering problem which involves both composition of relations and conjunction", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 644, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 658 + ], + "score": 1.0, + "content": "of queries. Future work includes experiments on natural question answering datasets and end-to-end", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 655, + 260, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 260, + 668 + ], + "score": 1.0, + "content": "training including the entity extractor.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 28.5 + }, + { + "type": "title", + "bbox": [ + 108, + 687, + 200, + 697 + ], + "lines": [ + { + "bbox": [ + 107, + 688, + 200, + 698 + ], + "spans": [ + { + "bbox": [ + 107, + 688, + 200, + 698 + ], + "score": 1.0, + "content": "ACKNOWLEDGMENTS", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 709, + 503, + 731 + ], + "lines": [ + { + "bbox": [ + 105, + 708, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 708, + 505, + 722 + ], + "score": 1.0, + "content": "The authors would like to thank Daniel Tarlow, Nate Kushman, and Kevin Gimpel for valuable", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 720, + 157, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 157, + 733 + ], + "score": 1.0, + "content": "discussions.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 35.5 + } + ], + "page_idx": 8, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 107, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 107, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "9", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 100, + 511, + 264 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 110, + 80, + 493, + 92 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 112, + 78, + 495, + 94 + ], + "spans": [ + { + "bbox": [ + 112, + 78, + 495, + 94 + ], + "score": 1.0, + "content": "Table 2: Results of joint learning with path queries and conjunction queries on WorldCup2014.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 106, + 100, + 511, + 264 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 100, + 511, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 100, + 511, + 264 + ], + "score": 0.983, + "html": "
TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#Sample questionH@1(%）FilteredMean RankH@1(%）FilteredMean RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered Rank
1which club does alan pulido play for?88.591.1891.951.1196.641.0498.661.01
2what position does gonzalo higuain play?100.001.0098.111.0398.741.01100.001.00
3how old is samuel etoo?67.111.4490.791.1394.741.0897.371.04
4what is the jersey number of mario balotelli?45.001.8983.571.2297.141.0399.291.01
5which country is thomas mueller from ?94.401.0694.401.0696.801.0498.401.02
6which country is the soccer team fc porto based in ?98.481.0298.481.0293.941.0695.451.05
7who plays professionally at liverpool fc?95.121.1090.241.2098.371.0496.751.04
8which player is from iran?89.861.5176.812.0738.652.9699.521.00
9name a player who plays goalkeeper?98.961.0169.791.8242.715.52100.001.00
10which soccer club is based in mexico?22.0313.9430.518.846.7810.6616.9521.14
11where is the club that edin dzeko plays for ？52.633.8857.242.1047.372.2778.291.41
12name a soccer club that has a player from australia ?30.4312.0833.7011.4713.0411.6419.5717.57
Overall (Path Query)74.163.1177.392.5669.543.0285.943.52
13who plays forward for fc barcelona?97.551.0676.071.6693.251.2498.771.02
14who are the defenders on german national team?95.931.0669.922.3365.042.04100.001.00
15which player in ssc napoli is from argentina?88.811.1776.121.7688.811.3597.761.03
Overall(Conj. Query)94.291.0974.291.8983.571.5198.811.02
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(2014; 2015) proposed a question-answering model that embeds both questions and", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 302, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 505, + 315 + ], + "score": 1.0, + "content": "their answers to a common continuous vector space. Their method in Bordes et al. (2015) can", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 313, + 505, + 325 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 325 + ], + "score": 1.0, + "content": "combine multiple knowledge bases and even generalize to a knowledge base that was not used", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 324, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 505, + 336 + ], + "score": 1.0, + "content": "during training. 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Another interesting connection to our work is that they take the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 451, + 506, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 506, + 463 + ], + "score": 1.0, + "content": "maximum of the inner-product scores (see also Weston et al., 2013; Neelakantan et al., 2015b),", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 461, + 506, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 506, + 474 + ], + "score": 1.0, + "content": "which are computed along multiple paths connecting a pair of entities. Representing a set as a", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "score": 1.0, + "content": "collection of vectors and taking the maximum over the inner-product scores is a natural way to", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 484, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 505, + 496 + ], + "score": 1.0, + "content": "represent a set of memory items. The Gaussian attention model we propose in this paper, however,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 494, + 333, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 333, + 507 + ], + "score": 1.0, + "content": "has the advantage of differentiability and composability.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 16.5, + "bbox_fs": [ + 105, + 374, + 506, + 507 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 528, + 195, + 540 + ], + "lines": [ + { + "bbox": [ + 104, + 525, + 197, + 543 + ], + "spans": [ + { + "bbox": [ + 104, + 525, + 197, + 543 + ], + "score": 1.0, + "content": "6 CONCLUSION", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 107, + 556, + 505, + 667 + ], + "lines": [ + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "score": 1.0, + "content": "In this paper, we have proposed the Gaussian attention model which can be used in a variety of", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 568, + 505, + 580 + ], + "spans": [ + { + "bbox": [ + 105, + 568, + 505, + 580 + ], + "score": 1.0, + "content": "contexts where we can assume that the distance between the memory items in the latent space is", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 577, + 506, + 592 + ], + "spans": [ + { + "bbox": [ + 104, + 577, + 506, + 592 + ], + "score": 1.0, + "content": "compatible with some notion of semantics. We have shown that the proposed Gaussian scoring", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 590, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 590, + 505, + 603 + ], + "score": 1.0, + "content": "function can be used for knowledge base embedding achieving competitive accuracy. We have also", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 601, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 506, + 613 + ], + "score": 1.0, + "content": "shown that our embedding model can naturally propagate uncertainty when we compose relations", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 612, + 505, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 612, + 505, + 623 + ], + "score": 1.0, + "content": "together. Our embedding model also benefits from compositional training proposed by Guu et al.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 623, + 504, + 634 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 504, + 634 + ], + "score": 1.0, + "content": "(2015). Furthermore, we have demonstrated the power of the Gaussian attention model in a chal-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 633, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 505, + 646 + ], + "score": 1.0, + "content": "lenging question answering problem which involves both composition of relations and conjunction", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 644, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 658 + ], + "score": 1.0, + "content": "of queries. Future work includes experiments on natural question answering datasets and end-to-end", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 655, + 260, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 260, + 668 + ], + "score": 1.0, + "content": "training including the entity extractor.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 28.5, + "bbox_fs": [ + 104, + 556, + 506, + 668 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 687, + 200, + 697 + ], + "lines": [ + { + "bbox": [ + 107, + 688, + 200, + 698 + ], + "spans": [ + { + "bbox": [ + 107, + 688, + 200, + 698 + ], + "score": 1.0, + "content": "ACKNOWLEDGMENTS", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 709, + 503, + 731 + ], + "lines": [ + { + "bbox": [ + 105, + 708, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 708, + 505, + 722 + ], + "score": 1.0, + "content": "The authors would like to thank Daniel Tarlow, Nate Kushman, and Kevin Gimpel for valuable", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 720, + 157, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 157, + 733 + ], + "score": 1.0, + "content": "discussions.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 35.5, + "bbox_fs": [ + 105, + 708, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 176, + 94 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 176, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 176, + 94 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 100, + 504, + 123 + ], + "lines": [ + { + "bbox": [ + 106, + 99, + 505, + 113 + ], + "spans": [ + { + "bbox": [ + 106, + 99, + 505, + 113 + ], + "score": 1.0, + "content": "Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 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SubjectRelationObject
david_villaplays-for_countryspain
lionel_messiplays_in-clubfc_barcelona
antoine-griezmannplays-positionforward
cristiano_ronaldowears_number7
fulham_fcis_in_countryengland
lukas_podolskiis_aged29
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#entity# atomic relations# atomic triplets112763977
#relations (atomic and compositional) in path queries# question and answer pairs in path queries(train/validation/ test）125620/804/1579
# types of questions in conjunctive queries# question and answer pairs in conjunctive queries(train/validation/test )31564/224/420
size of vocabulary1781
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#Query templateQuestion template
1Finde ∈ε:((player),plays_in_club,e)is truewhich club does (player) play for ?which professional football team does (player) play for ?which football club does (player) play for ?
2Finde∈ε:(player),plays-position,e)is truewhat position does (player) play ?
3Find e ∈ε:(player),is-aged,e) is truehow old is (player) ?what is the age of (player) ?
4Finde∈ε:(player),wears_number,e) is truewhat is the jersey number of (player) ?what number does (player) wear ?
5Finde ∈ε:(player),plays_for_country,e) is truewhat is the nationality of (player) ?which national team does (player) play for ?which country is (player) from ?
6Finde∈ε:(club),is-in_country,e)is truewhich country is the soccer team (club) based in ?
7Finde ∈ε: (club),plays_in_club-1,e)is truename a player from (club) ?who plays at the soccer club (club) ?who is from the professional football team (club) ?who plays professionally at (club) ?
8Finde ∈ε:(country-1),plays_for-country-1,e)is truewhich player is from (country_1) ?name a player from (country-1) ?who is from (country-1) ?who plays for the (country_1) national football team ?
9Finde∈ε:(position),playsposition-,e)is truename a player who plays (position) ?who plays (position) ?
10Finde ∈ε:(cotry-1),sicountry-1,e)is truewhich soccer club is based in (country_1) ?name a soccer club in (country_1) ?
11Finde∈ε:(player),plays_in_club /is_in_country,e)is truewhich country does (player) play professionally in ?where is the football club that (player) plays for ?
12Finde ∈ε:(country-1),plays-for-country-1/plays_in_club,e)is truewhich professional football team do players from (country_1) play for ？name a soccer club that has a player from (country_1) ?which professional football team has a player from (country_1) ?
13Find e∈ ε:(position),plays-position-1,e) is true and((club),plays-in_club-1,e) is truewho plays (position) for (club)?who are the (position) at (club) ?name a (position) that plays for (club) ?
14Find e∈ε: (position),plays-position-1,e) is true and(country-l),plays-for-country-1,e)is truewho plays (position) for (country_1) ?who are the (position) on (country_1) national team ?name a (position) from (country-1) ?which (country_2) footballer plays (position) ?name a (country-2) (position) ?
15Find e∈ε:(club)， plays_in_club-1,e) is true and(country_l),plays_for_country-1,e)is truewho are the (country_2) playersat (club)？which (country_2) footballer plays for (club) ?name a (country_2) player at (club) ?which player in (club) is from (country-1) ?
", + "type": "table", + "image_path": "5c8936e2f39543c1538d4f7c684c5e78d08c0646e6073693b5ca4bc83415e80b.jpg" + } + ] + } + ], + "index": 14, + "virtual_lines": [ + { + "bbox": [ + 106, + 400, + 529, + 506.6666666666667 + ], + "spans": [], + "index": 13 + }, + { + "bbox": [ + 106, + 506.6666666666667, + 529, + 613.3333333333334 + ], + "spans": [], + "index": 14 + }, + { + "bbox": [ + 106, + 613.3333333333334, + 529, + 720.0 + ], + "spans": [], + "index": 15 + } + ] + } + ], + "index": 12.5 + } + ], + "page_idx": 11, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "12", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 259, + 93 + ], + "lines": [ + { + "bbox": [ + 106, + 80, + 261, + 96 + ], + "spans": [ + { + "bbox": [ + 106, + 80, + 261, + 96 + ], + "score": 1.0, + "content": "A WORDCUP2014 DATASET", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 208, + 136, + 401, + 196 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 241, + 116, + 370, + 128 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 240, + 114, + 370, + 129 + ], + "spans": [ + { + "bbox": [ + 240, + 114, + 370, + 129 + ], + "score": 1.0, + "content": "Table 3: Sample atomic triplets.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "table_body", + "bbox": [ + 208, + 136, + 401, + 196 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 208, + 136, + 401, + 196 + ], + "spans": [ + { + "bbox": [ + 208, + 136, + 401, + 196 + ], + "score": 0.959, + "html": "
SubjectRelationObject
david_villaplays-for_countryspain
lionel_messiplays_in-clubfc_barcelona
antoine-griezmannplays-positionforward
cristiano_ronaldowears_number7
fulham_fcis_in_countryengland
lukas_podolskiis_aged29
", + "type": "table", + "image_path": "c76b54d069c446a577d193f3e4e7991307a9815e447eeaf69529984549fe539d.jpg" + } + ] + } + ], + "index": 3.5, + "virtual_lines": [ + { + "bbox": [ + 208, + 136, + 401, + 151.0 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 208, + 151.0, + 401, + 166.0 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 208, + 166.0, + 401, + 181.0 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 208, + 181.0, + 401, + 196.0 + ], + "spans": [], + "index": 5 + } + ] + } + ], + "index": 2.25 + }, + { + "type": "table", + "bbox": [ + 161, + 265, + 448, + 333 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 208, + 244, + 402, + 256 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 207, + 243, + 403, + 257 + ], + "spans": [ + { + "bbox": [ + 207, + 243, + 403, + 257 + ], + "score": 1.0, + "content": "Table 4: Statistics of the WorldCup2014 dataset.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "table_body", + "bbox": [ + 161, + 265, + 448, + 333 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 161, + 265, + 448, + 333 + ], + "spans": [ + { + "bbox": [ + 161, + 265, + 448, + 333 + ], + "score": 0.98, + "html": "
#entity# atomic relations# atomic triplets112763977
#relations (atomic and compositional) in path queries# question and answer pairs in path queries(train/validation/ test）125620/804/1579
# types of questions in conjunctive queries# question and answer pairs in conjunctive queries(train/validation/test )31564/224/420
size of vocabulary1781
", + "type": "table", + "image_path": "2745f1e997fc7c77d598f00975f60d1aef2225ce169b2b4d4728c20044684904.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 161, + 265, + 448, + 287.6666666666667 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 161, + 287.6666666666667, + 448, + 310.33333333333337 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 161, + 310.33333333333337, + 448, + 333.00000000000006 + ], + "spans": [], + "index": 9 + } + ] + } + ], + "index": 7.0 + }, + { + "type": "table", + "bbox": [ + 106, + 400, + 529, + 720 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 108, + 357, + 506, + 390 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 106, + 356, + 506, + 371 + ], + "spans": [ + { + "bbox": [ + 106, + 356, + 506, + 371 + ], + "score": 1.0, + "content": "Table 5: Templates of questions. In the table, (player), (club), (position) are placeholders of named", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 368, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 106, + 368, + 505, + 380 + ], + "score": 1.0, + "content": "entities with associated type. (country 1) is a placeholder for a country name while (country 2) is a", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 378, + 300, + 393 + ], + "spans": [ + { + "bbox": [ + 106, + 378, + 300, + 393 + ], + "score": 1.0, + "content": "placeholder for the adjectival form of a country.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11 + }, + { + "type": "table_body", + "bbox": [ + 106, + 400, + 529, + 720 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 106, + 400, + 529, + 720 + ], + "spans": [ + { + "bbox": [ + 106, + 400, + 529, + 720 + ], + "score": 0.984, + "html": "
#Query templateQuestion template
1Finde ∈ε:((player),plays_in_club,e)is truewhich club does (player) play for ?which professional football team does (player) play for ?which football club does (player) play for ?
2Finde∈ε:(player),plays-position,e)is truewhat position does (player) play ?
3Find e ∈ε:(player),is-aged,e) is truehow old is (player) ?what is the age of (player) ?
4Finde∈ε:(player),wears_number,e) is truewhat is the jersey number of (player) ?what number does (player) wear ?
5Finde ∈ε:(player),plays_for_country,e) is truewhat is the nationality of (player) ?which national team does (player) play for ?which country is (player) from ?
6Finde∈ε:(club),is-in_country,e)is truewhich country is the soccer team (club) based in ?
7Finde ∈ε: (club),plays_in_club-1,e)is truename a player from (club) ?who plays at the soccer club (club) ?who is from the professional football team (club) ?who plays professionally at (club) ?
8Finde ∈ε:(country-1),plays_for-country-1,e)is truewhich player is from (country_1) ?name a player from (country-1) ?who is from (country-1) ?who plays for the (country_1) national football team ?
9Finde∈ε:(position),playsposition-,e)is truename a player who plays (position) ?who plays (position) ?
10Finde ∈ε:(cotry-1),sicountry-1,e)is truewhich soccer club is based in (country_1) ?name a soccer club in (country_1) ?
11Finde∈ε:(player),plays_in_club /is_in_country,e)is truewhich country does (player) play professionally in ?where is the football club that (player) plays for ?
12Finde ∈ε:(country-1),plays-for-country-1/plays_in_club,e)is truewhich professional football team do players from (country_1) play for ？name a soccer club that has a player from (country_1) ?which professional football team has a player from (country_1) ?
13Find e∈ ε:(position),plays-position-1,e) is true and((club),plays-in_club-1,e) is truewho plays (position) for (club)?who are the (position) at (club) ?name a (position) that plays for (club) ?
14Find e∈ε: (position),plays-position-1,e) is true and(country-l),plays-for-country-1,e)is truewho plays (position) for (country_1) ?who are the (position) on (country_1) national team ?name a (position) from (country-1) ?which (country_2) footballer plays (position) ?name a (country-2) (position) ?
15Find e∈ε:(club)， plays_in_club-1,e) is true and(country_l),plays_for_country-1,e)is truewho are the (country_2) playersat (club)？which (country_2) footballer plays for (club) ?name a (country_2) player at (club) ?which player in (club) is from (country-1) ?
", + "type": "table", + "image_path": "5c8936e2f39543c1538d4f7c684c5e78d08c0646e6073693b5ca4bc83415e80b.jpg" + } + ] + } + ], + "index": 14, + "virtual_lines": [ + { + "bbox": [ + 106, + 400, + 529, + 506.6666666666667 + ], + "spans": [], + "index": 13 + }, + { + "bbox": [ + 106, + 506.6666666666667, + 529, + 613.3333333333334 + ], + "spans": [], + "index": 14 + }, + { + "bbox": [ + 106, + 613.3333333333334, + 529, + 720.0 + ], + "spans": [], + "index": 15 + } + ] + } + ], + "index": 12.5 + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 101, + 540, + 269 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 166, + 81, + 441, + 92 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 166, + 79, + 441, + 94 + ], + "spans": [ + { + "bbox": [ + 166, + 79, + 441, + 94 + ], + "score": 1.0, + "content": "Table 6: (Composed) relations and sample questions in path queries.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 106, + 101, + 540, + 269 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 101, + 540, + 269 + ], + "spans": [ + { + "bbox": [ + 106, + 101, + 540, + 269 + ], + "score": 0.983, + "html": "
#RelationTypeSample questionSample answer
1plays_in_clubmany-to-onewhich club doesalan pulido play for ?which professional footbal team does klaas jan huntelar play for ?tigres_uanlfc_schalke_04
2plays-positionmany-to-onewhat position does gonzalo higuain play ?ssc_napoli
3is_agedmany-to-onehow old is samuel etoo ?what is the age of luis suarez ?3
4wears-numbermany-to-onewhat is the jersey number of mario balotelli ?what number does shinji okazaki wear ?：
5plays_for_countrymany-to-onewhich country is thomas mueller from ?what is the nationality of helder postiga ?germanyportugal
6is.in_countrymany-to-onewhich country is the soccer team fc porto based in ?portugal
7plays_in_club-1one-to-manywho playsprofessionally at liverpool fc ?name a player from as roma ?steven_gerrardmiralem_pjanic
8plays-for_country-1one-to-manywhich player is from iran ？name a player from italy ?masoud_shojaeidaniele_de_rossi
9plays-position-1one-to-manyname a player who plays goalkeeper ?who plays forward ?gianluiqi-buffonraul_jimenez
10is_in-country-1one-to-manywhich soccer club is based in mexico ?name a soccer club in australia ?cruz_azul.fcmelbourne_victory_fc
11plays_in_club /is_in_countrymany-to-onewhere is the club that edin dzeko plays for ?which country does sime vrsaljko play professionally in ?englanditaly
12plays-for_country-1/plays_in_clubmany-to-manyname a soccer club that has a player from australia?name a soccer club that has a player from spain ?crystal_palace_fcfc_barcelona
", + "type": "table", + "image_path": "1e08d92fcdcdcb4612cfc8a344544f32e1c03b71996f84931a70e6d731e7a783.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 106, + 101, + 540, + 157.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 106, + 157.0, + 540, + 213.0 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 106, + 213.0, + 540, + 269.0 + ], + "spans": [], + "index": 3 + } + ] + } + ], + "index": 1.0 + }, + { + "type": "table", + "bbox": [ + 107, + 300, + 573, + 374 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 201, + 280, + 405, + 292 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 199, + 279, + 407, + 294 + ], + "spans": [ + { + "bbox": [ + 199, + 279, + 407, + 294 + ], + "score": 1.0, + "content": "Table 7: Conjunctive queries and sample questions.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "table_body", + "bbox": [ + 107, + 300, + 573, + 374 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 107, + 300, + 573, + 374 + ], + "spans": [ + { + "bbox": [ + 107, + 300, + 573, + 374 + ], + "score": 0.979, + "html": "
#RelationsSample questionsEntities in questionsSampleanswer
13plays_position-1 and plays_in_club-1who plays forward for fc barcelona ? who are the midfielders at fc bayern muenchen ?forward,fc_barcelona midfielder,fc_bayern_muenchenlionel_messi toni_kroos
14plays-position -1 andwho are the defenders on german national team ? which mexican footballer plays forward ?defender,germany defender,mexicoper_mertesacker raul-jimenez
15plays_in_club-1 and plays_for_country -1which player in paris saint-germain fc is from argentina ? who are the korean players at beijing guoan ?paris_saint-germain_fc,argentina beijing-guoan,koreaezequiel_lavezzi ha-daesung
", + "type": "table", + "image_path": "612204b4a493e4e6ad7548f7a46ce07e9418c499cd0449151d472e0148446f5f.jpg" + } + ] + } + ], + "index": 6, + "virtual_lines": [ + { + "bbox": [ + 107, + 300, + 573, + 324.6666666666667 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 107, + 324.6666666666667, + 573, + 349.33333333333337 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 107, + 349.33333333333337, + 573, + 374.00000000000006 + ], + "spans": [], + "index": 7 + } + ] + } + ], + "index": 5.0 + }, + { + "type": "title", + "bbox": [ + 108, + 393, + 392, + 406 + ], + "lines": [ + { + "bbox": [ + 105, + 393, + 393, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 393, + 408 + ], + "score": 1.0, + "content": "B TRANSGAUSSIAN EMBEDDING OF WORLDCUP2014", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 106, + 419, + 505, + 583 + ], + "lines": [ + { + "bbox": [ + 106, + 418, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 106, + 418, + 505, + 431 + ], + "score": 1.0, + "content": "We trained our TransGaussian model on triplets and paths from WorldCup2014 dataset and illus-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "trated the embeddings in Fig 3 and 4. Recall that we modeled every relation as a Gaussian with", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 441, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 505, + 453 + ], + "score": 1.0, + "content": "diagonal covariance matrix. Fig 3 shows the learned variance parameters of different relations. Each", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 452, + 504, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 504, + 464 + ], + "score": 1.0, + "content": "row corresponds to the variances of one relation. Columns are permuted to reveal the block struc-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "ture. From this figure, we can see that every relation has a small variance in two or more dimensions.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "score": 1.0, + "content": "This implies that the coordinates of the embedding space are partitioned into semantically coherent", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 484, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 505, + 497 + ], + "score": 1.0, + "content": "clusters each of which represent a particular attribute of a player (or a football club). To verify this", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 495, + 506, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 506, + 508 + ], + "score": 1.0, + "content": "further, we picked the two coordinates in which a relation (e.g. plays position) has the least", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "variance and projected the embedding of all valid subjects and objects (e.g. players and positions)", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 516, + 506, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 506, + 530 + ], + "score": 1.0, + "content": "of the relation to this 2 dimensional subspace. See Fig. 4. The relation between the subjects and the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 528, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 505, + 541 + ], + "score": 1.0, + "content": "objects are simply translation in the projection when the corresponding subspace is two dimensional", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 540, + 506, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 506, + 552 + ], + "score": 1.0, + "content": "(e.g., plays position relation in Fig. 4 (a)). The same is true for other relations that requires", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 550, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 505, + 562 + ], + "score": 1.0, + "content": "larger dimension but it is more challenging to visualize in two dimensions. For relations that have", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 561, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 505, + 574 + ], + "score": 1.0, + "content": "a large number of unique objects, we only plotted for the eight objects with the most subjects for", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 572, + 194, + 585 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 194, + 585 + ], + "score": 1.0, + "content": "clarity of illustration.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 589, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 589, + 505, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 589, + 505, + 601 + ], + "score": 1.0, + "content": "Furthermore, in order to elucidate whether we are limited by the capacity of the TransGaussian", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 600, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 600, + 506, + 613 + ], + "score": 1.0, + "content": "embedding or the ability to decode question expressed in natural language, we evaluated the test", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 611, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 505, + 624 + ], + "score": 1.0, + "content": "question-answer pairs using the TransGaussian embedding composed according to the ground-truth", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "score": 1.0, + "content": "relations and entities. The results were evaluated with the same metrics as in Sec. 4.3. This es-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 632, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 506, + 646 + ], + "score": 1.0, + "content": "timation is conducted for TransE embeddings as well. See Table 8 for the results. Compared to", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 643, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 505, + 657 + ], + "score": 1.0, + "content": "Table 2, the accuracy of TransGaussian (COMP) is higher on the atomic relations and path queries", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "score": 1.0, + "content": "but lower on conjunctive queries. This is natural because when the query is simple there is not", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 665, + 506, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 506, + 680 + ], + "score": 1.0, + "content": "much room for the question-answering network to improve upon just combining the relations ac-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 678, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 504, + 689 + ], + "score": 1.0, + "content": "cording to the ground truth relations, whereas when the query is complex the network could com-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 687, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 701 + ], + "score": 1.0, + "content": "bine the embedding in a more creative way to overcome its limitation. In fact, the two queries", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "(#10 and #12) that TransGaussian (COMP) did not perform well in Table 2 pertain to a single re-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 708, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 708, + 486, + 723 + ], + "score": 1.0, + "content": "lation is in country−1 (#10) and a composition of two relations plays for country", + "type": "text" + }, + { + "bbox": [ + 486, + 709, + 505, + 721 + ], + "score": 0.31, + "content": "^ - 1 \\ /", + "type": "inline_equation" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "score": 1.0, + "content": "plays in club (#12). The performance of the two queries were low even when the ground truth", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30 + } + ], + "page_idx": 12, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "score": 1.0, + "content": "13", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 101, + 540, + 269 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 166, + 81, + 441, + 92 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 166, + 79, + 441, + 94 + ], + "spans": [ + { + "bbox": [ + 166, + 79, + 441, + 94 + ], + "score": 1.0, + "content": "Table 6: (Composed) relations and sample questions in path queries.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 106, + 101, + 540, + 269 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 101, + 540, + 269 + ], + "spans": [ + { + "bbox": [ + 106, + 101, + 540, + 269 + ], + "score": 0.983, + "html": "
#RelationTypeSample questionSample answer
1plays_in_clubmany-to-onewhich club doesalan pulido play for ?which professional footbal team does klaas jan huntelar play for ?tigres_uanlfc_schalke_04
2plays-positionmany-to-onewhat position does gonzalo higuain play ?ssc_napoli
3is_agedmany-to-onehow old is samuel etoo ?what is the age of luis suarez ?3
4wears-numbermany-to-onewhat is the jersey number of mario balotelli ?what number does shinji okazaki wear ?：
5plays_for_countrymany-to-onewhich country is thomas mueller from ?what is the nationality of helder postiga ?germanyportugal
6is.in_countrymany-to-onewhich country is the soccer team fc porto based in ?portugal
7plays_in_club-1one-to-manywho playsprofessionally at liverpool fc ?name a player from as roma ?steven_gerrardmiralem_pjanic
8plays-for_country-1one-to-manywhich player is from iran ？name a player from italy ?masoud_shojaeidaniele_de_rossi
9plays-position-1one-to-manyname a player who plays goalkeeper ?who plays forward ?gianluiqi-buffonraul_jimenez
10is_in-country-1one-to-manywhich soccer club is based in mexico ?name a soccer club in australia ?cruz_azul.fcmelbourne_victory_fc
11plays_in_club /is_in_countrymany-to-onewhere is the club that edin dzeko plays for ?which country does sime vrsaljko play professionally in ?englanditaly
12plays-for_country-1/plays_in_clubmany-to-manyname a soccer club that has a player from australia?name a soccer club that has a player from spain ?crystal_palace_fcfc_barcelona
", + "type": "table", + "image_path": "1e08d92fcdcdcb4612cfc8a344544f32e1c03b71996f84931a70e6d731e7a783.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 106, + 101, + 540, + 157.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 106, + 157.0, + 540, + 213.0 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 106, + 213.0, + 540, + 269.0 + ], + "spans": [], + "index": 3 + } + ] + } + ], + "index": 1.0 + }, + { + "type": "table", + "bbox": [ + 107, + 300, + 573, + 374 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 201, + 280, + 405, + 292 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 199, + 279, + 407, + 294 + ], + "spans": [ + { + "bbox": [ + 199, + 279, + 407, + 294 + ], + "score": 1.0, + "content": "Table 7: Conjunctive queries and sample questions.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "table_body", + "bbox": [ + 107, + 300, + 573, + 374 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 107, + 300, + 573, + 374 + ], + "spans": [ + { + "bbox": [ + 107, + 300, + 573, + 374 + ], + "score": 0.979, + "html": "
#RelationsSample questionsEntities in questionsSampleanswer
13plays_position-1 and plays_in_club-1who plays forward for fc barcelona ? who are the midfielders at fc bayern muenchen ?forward,fc_barcelona midfielder,fc_bayern_muenchenlionel_messi toni_kroos
14plays-position -1 andwho are the defenders on german national team ? which mexican footballer plays forward ?defender,germany defender,mexicoper_mertesacker raul-jimenez
15plays_in_club-1 and plays_for_country -1which player in paris saint-germain fc is from argentina ? who are the korean players at beijing guoan ?paris_saint-germain_fc,argentina beijing-guoan,koreaezequiel_lavezzi ha-daesung
", + "type": "table", + "image_path": "612204b4a493e4e6ad7548f7a46ce07e9418c499cd0449151d472e0148446f5f.jpg" + } + ] + } + ], + "index": 6, + "virtual_lines": [ + { + "bbox": [ + 107, + 300, + 573, + 324.6666666666667 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 107, + 324.6666666666667, + 573, + 349.33333333333337 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 107, + 349.33333333333337, + 573, + 374.00000000000006 + ], + "spans": [], + "index": 7 + } + ] + } + ], + "index": 5.0 + }, + { + "type": "title", + "bbox": [ + 108, + 393, + 392, + 406 + ], + "lines": [ + { + "bbox": [ + 105, + 393, + 393, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 393, + 408 + ], + "score": 1.0, + "content": "B TRANSGAUSSIAN EMBEDDING OF WORLDCUP2014", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 106, + 419, + 505, + 583 + ], + "lines": [ + { + "bbox": [ + 106, + 418, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 106, + 418, + 505, + 431 + ], + "score": 1.0, + "content": "We trained our TransGaussian model on triplets and paths from WorldCup2014 dataset and illus-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "trated the embeddings in Fig 3 and 4. Recall that we modeled every relation as a Gaussian with", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 441, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 505, + 453 + ], + "score": 1.0, + "content": "diagonal covariance matrix. Fig 3 shows the learned variance parameters of different relations. Each", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 452, + 504, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 504, + 464 + ], + "score": 1.0, + "content": "row corresponds to the variances of one relation. Columns are permuted to reveal the block struc-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "ture. From this figure, we can see that every relation has a small variance in two or more dimensions.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "score": 1.0, + "content": "This implies that the coordinates of the embedding space are partitioned into semantically coherent", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 484, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 505, + 497 + ], + "score": 1.0, + "content": "clusters each of which represent a particular attribute of a player (or a football club). To verify this", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 495, + 506, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 506, + 508 + ], + "score": 1.0, + "content": "further, we picked the two coordinates in which a relation (e.g. plays position) has the least", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "variance and projected the embedding of all valid subjects and objects (e.g. players and positions)", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 516, + 506, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 506, + 530 + ], + "score": 1.0, + "content": "of the relation to this 2 dimensional subspace. See Fig. 4. The relation between the subjects and the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 528, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 505, + 541 + ], + "score": 1.0, + "content": "objects are simply translation in the projection when the corresponding subspace is two dimensional", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 540, + 506, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 506, + 552 + ], + "score": 1.0, + "content": "(e.g., plays position relation in Fig. 4 (a)). The same is true for other relations that requires", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 550, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 505, + 562 + ], + "score": 1.0, + "content": "larger dimension but it is more challenging to visualize in two dimensions. For relations that have", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 561, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 505, + 574 + ], + "score": 1.0, + "content": "a large number of unique objects, we only plotted for the eight objects with the most subjects for", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 572, + 194, + 585 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 194, + 585 + ], + "score": 1.0, + "content": "clarity of illustration.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 16, + "bbox_fs": [ + 105, + 418, + 506, + 585 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 589, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 589, + 505, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 589, + 505, + 601 + ], + "score": 1.0, + "content": "Furthermore, in order to elucidate whether we are limited by the capacity of the TransGaussian", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 600, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 600, + 506, + 613 + ], + "score": 1.0, + "content": "embedding or the ability to decode question expressed in natural language, we evaluated the test", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 611, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 505, + 624 + ], + "score": 1.0, + "content": "question-answer pairs using the TransGaussian embedding composed according to the ground-truth", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "score": 1.0, + "content": "relations and entities. The results were evaluated with the same metrics as in Sec. 4.3. This es-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 632, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 506, + 646 + ], + "score": 1.0, + "content": "timation is conducted for TransE embeddings as well. See Table 8 for the results. Compared to", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 643, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 505, + 657 + ], + "score": 1.0, + "content": "Table 2, the accuracy of TransGaussian (COMP) is higher on the atomic relations and path queries", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "score": 1.0, + "content": "but lower on conjunctive queries. This is natural because when the query is simple there is not", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 665, + 506, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 506, + 680 + ], + "score": 1.0, + "content": "much room for the question-answering network to improve upon just combining the relations ac-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 678, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 504, + 689 + ], + "score": 1.0, + "content": "cording to the ground truth relations, whereas when the query is complex the network could com-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 687, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 701 + ], + "score": 1.0, + "content": "bine the embedding in a more creative way to overcome its limitation. In fact, the two queries", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "(#10 and #12) that TransGaussian (COMP) did not perform well in Table 2 pertain to a single re-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 708, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 708, + 486, + 723 + ], + "score": 1.0, + "content": "lation is in country−1 (#10) and a composition of two relations plays for country", + "type": "text" + }, + { + "bbox": [ + 486, + 709, + 505, + 721 + ], + "score": 0.31, + "content": "^ - 1 \\ /", + "type": "inline_equation" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "score": 1.0, + "content": "plays in club (#12). The performance of the two queries were low even when the ground truth", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30, + "bbox_fs": [ + 104, + 589, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 151, + 85, + 468, + 195 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 151, + 85, + 468, + 195 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 151, + 85, + 468, + 195 + ], + "spans": [ + { + "bbox": [ + 151, + 85, + 468, + 195 + ], + "score": 0.963, + "type": "image", + "image_path": "dcac266cd0111b767c6f604dadfa93e9478ad13210e7862e4fc0a7fbd0595157.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 151, + 85, + 468, + 121.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 151, + 121.66666666666666, + 468, + 158.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 151, + 158.33333333333331, + 468, + 194.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 208, + 504, + 232 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 208, + 506, + 221 + ], + "spans": [ + { + "bbox": [ + 105, + 208, + 506, + 221 + ], + "score": 1.0, + "content": "Figure 3: Variance of each relation. Each row shows the diagonal values in the variance matrix", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 219, + 422, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 219, + 422, + 232 + ], + "score": 1.0, + "content": "associated with a relation. Columns are permuted to reveal the block structure.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "text", + "bbox": [ + 108, + 249, + 505, + 283 + ], + "lines": [ + { + "bbox": [ + 106, + 249, + 505, + 262 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 505, + 262 + ], + "score": 1.0, + "content": "Table 8: Evaluation of embeddings. We evaluate the embeddings by feeding the correct entities and", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 260, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 505, + 273 + ], + "score": 1.0, + "content": "relations from a path or conjunctive query to an embedding model and using its scoring function to", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 272, + 337, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 337, + 284 + ], + "score": 1.0, + "content": "retrieve the answers from the embedded knowledge base.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 106, + 290, + 527, + 521 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 106, + 290, + 527, + 521 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 290, + 527, + 521 + ], + "spans": [ + { + "bbox": [ + 106, + 290, + 527, + 521 + ], + "score": 0.984, + "html": "
TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#RelationH@1(%)Mean Filtered RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered Rank
1plays.in.club75.541.3893.481.0999.861.0098.511.02
2plays-position96.331.0494.021.0998.371.02100.001.00
3is_aged55.031.6991.441.1296.881.03100.001.00
4wears_number38.862.0978.671.3295.921.04100.001.00
5plays_for_country71.601.3994.841.1099.321.01100.001.00
6is_in_country98.321.0399.661.0099.331.01100.001.00
7plays_in_club-187.501.4683.421.4594.701.0797.421.03
882.471.6868.213.3725.275.6698.781.02
9plays-position-1100.001.0075.541.6013.5924.3598.781.02
10is_in-country-123.1126.9223.4823.278.32130.5919.4183.61
11plays_in_club/is_in-country20.247.0558.291.9846.882.9980.161.38
12plays-for_country -1/plays-in_club25.3222.2727.7310.0419.0435.5920.1533.01
Overall(Path relations) plays-position-164.645.0975.023.5967.2214.8786.738.79
13and plays-in_club-1 plays-position91.851.2069.971.8277.451.8395.381.06
14and plays_in_club =T91.711.2366.712.8551.494.8897.831.05
15and is_in_country -188.591.2073.37 70.021.80 2.1683.421.3494.701.08
Overall (Conj.relations)90.721.2170.792.6895.971.06
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(2015).", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "As done by Guu et al. (2015), we trained TransGaussian (SINGLE) with atomic triplets only and", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "trained TransGaussian (COMP) with the union of atomic triplets and paths. We did not incorporate", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22.5 + } + ], + "page_idx": 13, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 301, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 14 + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 107, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 107, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 151, + 85, + 468, + 195 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 151, + 85, + 468, + 195 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 151, + 85, + 468, + 195 + ], + "spans": [ + { + "bbox": [ + 151, + 85, + 468, + 195 + ], + "score": 0.963, + "type": "image", + "image_path": "dcac266cd0111b767c6f604dadfa93e9478ad13210e7862e4fc0a7fbd0595157.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 151, + 85, + 468, + 121.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 151, + 121.66666666666666, + 468, + 158.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 151, + 158.33333333333331, + 468, + 194.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 208, + 504, + 232 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 208, + 506, + 221 + ], + "spans": [ + { + "bbox": [ + 105, + 208, + 506, + 221 + ], + "score": 1.0, + "content": "Figure 3: Variance of each relation. Each row shows the diagonal values in the variance matrix", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 219, + 422, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 219, + 422, + 232 + ], + "score": 1.0, + "content": "associated with a relation. Columns are permuted to reveal the block structure.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "text", + "bbox": [ + 108, + 249, + 505, + 283 + ], + "lines": [ + { + "bbox": [ + 106, + 249, + 505, + 262 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 505, + 262 + ], + "score": 1.0, + "content": "Table 8: Evaluation of embeddings. We evaluate the embeddings by feeding the correct entities and", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 260, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 505, + 273 + ], + "score": 1.0, + "content": "relations from a path or conjunctive query to an embedding model and using its scoring function to", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 272, + 337, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 337, + 284 + ], + "score": 1.0, + "content": "retrieve the answers from the embedded knowledge base.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6, + "bbox_fs": [ + 105, + 249, + 505, + 284 + ] + }, + { + "type": "table", + "bbox": [ + 106, + 290, + 527, + 521 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 106, + 290, + 527, + 521 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 290, + 527, + 521 + ], + "spans": [ + { + "bbox": [ + 106, + 290, + 527, + 521 + ], + "score": 0.984, + "html": "
TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#RelationH@1(%)Mean Filtered RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered Rank
1plays.in.club75.541.3893.481.0999.861.0098.511.02
2plays-position96.331.0494.021.0998.371.02100.001.00
3is_aged55.031.6991.441.1296.881.03100.001.00
4wears_number38.862.0978.671.3295.921.04100.001.00
5plays_for_country71.601.3994.841.1099.321.01100.001.00
6is_in_country98.321.0399.661.0099.331.01100.001.00
7plays_in_club-187.501.4683.421.4594.701.0797.421.03
882.471.6868.213.3725.275.6698.781.02
9plays-position-1100.001.0075.541.6013.5924.3598.781.02
10is_in-country-123.1126.9223.4823.278.32130.5919.4183.61
11plays_in_club/is_in-country20.247.0558.291.9846.882.9980.161.38
12plays-for_country -1/plays-in_club25.3222.2727.7310.0419.0435.5920.1533.01
Overall(Path relations) plays-position-164.645.0975.023.5967.2214.8786.738.79
13and plays-in_club-1 plays-position91.851.2069.971.8277.451.8395.381.06
14and plays_in_club =T91.711.2366.712.8551.494.8897.831.05
15and is_in_country -188.591.2073.37 70.021.80 2.1683.421.3494.701.08
Overall (Conj.relations)90.721.2170.792.6895.971.06
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Without getting param-", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 625, + 505, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 625, + 505, + 637 + ], + "score": 1.0, + "content": "eters tuned too much, TransGaussian (COMP) obtained accuracy comparable to TransE (COMP).", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 637, + 163, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 637, + 163, + 647 + ], + "score": 1.0, + "content": "See Table 11.", + "type": "text", + "cross_page": true + } + ], + "index": 7 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 709, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 77, + 536, + 558 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 107, + 77, + 536, + 558 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 77, + 536, + 558 + ], + "spans": [ + { + "bbox": [ + 107, + 77, + 536, + 558 + ], + "score": 0.976, + "type": "image", + "image_path": "4a25b8273f36037ebd611825cf1990cec4dc4df993551c3f676718009d7fca5b.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 107, + 77, + 536, + 237.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 107, + 237.33333333333334, + 536, + 397.6666666666667 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 107, + 397.6666666666667, + 536, + 558.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 105, + 565, + 509, + 588 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 565, + 506, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 506, + 578 + ], + "score": 1.0, + "content": "Figure 4: TransGaussian entity embeddings. Crosses are the subjects and circles are the objects of a", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 576, + 459, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 459, + 588 + ], + "score": 1.0, + "content": "relation. Specifically, crosses are players in (a)-(e) and professional football clubs in (f).", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "text", + "bbox": [ + 107, + 614, + 506, + 648 + ], + "lines": [ + { + "bbox": [ + 105, + 613, + 505, + 627 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 505, + 627 + ], + "score": 1.0, + "content": "word embedding in this task and each entity is assigned its individual vector. Without getting param-", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 625, + 505, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 625, + 505, + 637 + ], + "score": 1.0, + "content": "eters tuned too much, TransGaussian (COMP) obtained accuracy comparable to TransE (COMP).", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 637, + 163, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 637, + 163, + 647 + ], + "score": 1.0, + "content": "See Table 11.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6 + } + ], + "page_idx": 14, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "15", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 77, + 536, + 558 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 107, + 77, + 536, + 558 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 77, + 536, + 558 + ], + "spans": [ + { + "bbox": [ + 107, + 77, + 536, + 558 + ], + "score": 0.976, + "type": "image", + "image_path": "4a25b8273f36037ebd611825cf1990cec4dc4df993551c3f676718009d7fca5b.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 107, + 77, + 536, + 237.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 107, + 237.33333333333334, + 536, + 397.6666666666667 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 107, + 397.6666666666667, + 536, + 558.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 105, + 565, + 509, + 588 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 565, + 506, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 506, + 578 + ], + "score": 1.0, + "content": "Figure 4: TransGaussian entity embeddings. Crosses are the subjects and circles are the objects of a", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 576, + 459, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 459, + 588 + ], + "score": 1.0, + "content": "relation. Specifically, crosses are players in (a)-(e) and professional football clubs in (f).", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "text", + "bbox": [ + 107, + 614, + 506, + 648 + ], + "lines": [], + "index": 6, + "bbox_fs": [ + 105, + 613, + 505, + 647 + ], + "lines_deleted": true + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 140, + 516, + 345 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 174, + 119, + 433, + 131 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 173, + 119, + 434, + 133 + ], + "spans": [ + { + "bbox": [ + 173, + 119, + 434, + 133 + ], + "score": 1.0, + "content": "Table 9: Experimental results of path queries on WorldCup2014.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 106, + 140, + 516, + 345 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 140, + 516, + 345 + ], + "spans": [ + { + "bbox": [ + 106, + 140, + 516, + 345 + ], + "score": 0.98, + "html": "
TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#Relation and sample questionMean H@1(%）Filtered RankH@1(%)Mean Filtered RankMean H@1(%) Filtered RankH@1(%)Mean Filtered Rank
1plays.in_club (which club does alan pulido play for?)90.60 1.1292.621.1196.64 1.0397.991.03
2plays-position (what position does gonzalo higuain play?)100.00 1.0098.111.0298.74 1.01100.001.00
3is_aged (how old is samuel etoo?)81.58 1.3092.111.1096.05 1.04100.001.00
4wears_number (what is the jersey number of mario balotelli?)44.29 1.8885.711.1996.43 1.04100.001.00
5plays-for-country (which country is thomas mueller from ?)97.60 1.0294.401.1198.40 1.0299.201.01
6is_in.country (which country is the soccer team fc porto based in ?)98.48 1.0298.481.0293.94 1.0898.481.02
7plays_in_club-1 (who plays professionally at liverpool fc?)95.12 1.0886.991.3896.75 1.0396.751.03
8plays_for_country (which player is from iran?)81.16 1.6172.462.3640.58 3.1993.241.48
9plays-position (name a player who plays goalkeeper?)100.00 1.0030.212.3055.21 5.0985.421.15
10is.in_country (which soccer club is based in mexico?)24.58 11.4723.7310.075.08 9.1817.8020.10
11plays_in_club/is_in_country (where is the club that edin dzeko plays for ?)48.68 4.2462.502.0748.03 2.4176.971.50
12plays-for-country-1/plays-in-club (name a soccer club that hasaplayer from australia ?)34.78 9.4930.4311.266.52 9.8816.3020.27
Overall74.92 2.8074.352.7170.172.82 84.423.68
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TransE(SINGLE)TransE(COMP)TransGaussian(SINGLE)TransGaussian(COMP)
#Relation and sample questionMeanH@1(%)FilteredRankMeanH@1(%)FilteredRankMeanH@1(%)FilteredRankMeanH@1(%)FilteredRank
13(who plays forward for fc barcelona?)94.48 1.1071.17 1.7787.12 1.3798.77 1.02
14plays-position-and plays-for-country-1(who are the defenders on german national team?)95.93 1.0876.42 2.5064.23 2.02100.00 1.00
15plays_in_club-1andis_in_country(which player in ssc napoli is from argentina?)91.79 1.1375.37 1.7588.06 1.3794.03 1.07
Overall94.05 1.1174.05 1.9780.71 1.5697.62 1.03
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ModelAccuracy (%)
TransE (SINGLE)68.5
TransE (COMP)80.3
TransGaussian (SINGLE)58.4
TransGaussian (COMP)76.4
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TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#Relation and sample questionMean H@1(%）Filtered RankH@1(%)Mean Filtered RankMean H@1(%) Filtered RankH@1(%)Mean Filtered Rank
1plays.in_club (which club does alan pulido play for?)90.60 1.1292.621.1196.64 1.0397.991.03
2plays-position (what position does gonzalo higuain play?)100.00 1.0098.111.0298.74 1.01100.001.00
3is_aged (how old is samuel etoo?)81.58 1.3092.111.1096.05 1.04100.001.00
4wears_number (what is the jersey number of mario balotelli?)44.29 1.8885.711.1996.43 1.04100.001.00
5plays-for-country (which country is thomas mueller from ?)97.60 1.0294.401.1198.40 1.0299.201.01
6is_in.country (which country is the soccer team fc porto based in ?)98.48 1.0298.481.0293.94 1.0898.481.02
7plays_in_club-1 (who plays professionally at liverpool fc?)95.12 1.0886.991.3896.75 1.0396.751.03
8plays_for_country (which player is from iran?)81.16 1.6172.462.3640.58 3.1993.241.48
9plays-position (name a player who plays goalkeeper?)100.00 1.0030.212.3055.21 5.0985.421.15
10is.in_country (which soccer club is based in mexico?)24.58 11.4723.7310.075.08 9.1817.8020.10
11plays_in_club/is_in_country (where is the club that edin dzeko plays for ?)48.68 4.2462.502.0748.03 2.4176.971.50
12plays-for-country-1/plays-in-club (name a soccer club that hasaplayer from australia ?)34.78 9.4930.4311.266.52 9.8816.3020.27
Overall74.92 2.8074.352.7170.172.82 84.423.68
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TransE(SINGLE)TransE(COMP)TransGaussian(SINGLE)TransGaussian(COMP)
#Relation and sample questionMeanH@1(%)FilteredRankMeanH@1(%)FilteredRankMeanH@1(%)FilteredRankMeanH@1(%)FilteredRank
13(who plays forward for fc barcelona?)94.48 1.1071.17 1.7787.12 1.3798.77 1.02
14plays-position-and plays-for-country-1(who are the defenders on german national team?)95.93 1.0876.42 2.5064.23 2.02100.00 1.00
15plays_in_club-1andis_in_country(which player in ssc napoli is from argentina?)91.79 1.1375.37 1.7588.06 1.3794.03 1.07
Overall94.05 1.1174.05 1.9780.71 1.5697.62 1.03
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ModelAccuracy (%)
TransE (SINGLE)68.5
TransE (COMP)80.3
TransGaussian (SINGLE)58.4
TransGaussian (COMP)76.4
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# entity
#atomic relations# atomic triplets
# path query Q&A（train/validation/test）# conjunctive query Q&A（train /validation /test）
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TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#Sample questionH@1(%）FilteredMean RankH@1(%）FilteredMean RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered Rank
1which club does alan pulido play for?88.591.1891.951.1196.641.0498.661.01
2what position does gonzalo higuain play?100.001.0098.111.0398.741.01100.001.00
3how old is samuel etoo?67.111.4490.791.1394.741.0897.371.04
4what is the jersey number of mario balotelli?45.001.8983.571.2297.141.0399.291.01
5which country is thomas mueller from ?94.401.0694.401.0696.801.0498.401.02
6which country is the soccer team fc porto based in ?98.481.0298.481.0293.941.0695.451.05
7who plays professionally at liverpool fc?95.121.1090.241.2098.371.0496.751.04
8which player is from iran?89.861.5176.812.0738.652.9699.521.00
9name a player who plays goalkeeper?98.961.0169.791.8242.715.52100.001.00
10which soccer club is based in mexico?22.0313.9430.518.846.7810.6616.9521.14
11where is the club that edin dzeko plays for ？52.633.8857.242.1047.372.2778.291.41
12name a soccer club that has a player from australia ?30.4312.0833.7011.4713.0411.6419.5717.57
Overall (Path Query)74.163.1177.392.5669.543.0285.943.52
13who plays forward for fc barcelona?97.551.0676.071.6693.251.2498.771.02
14who are the defenders on german national team?95.931.0669.922.3365.042.04100.001.00
15which player in ssc napoli is from argentina?88.811.1776.121.7688.811.3597.761.03
Overall(Conj. Query)94.291.0974.291.8983.571.5198.811.02
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#Query templateQuestion template
1Finde ∈ε:((player),plays_in_club,e)is truewhich club does (player) play for ?which professional football team does (player) play for ?which football club does (player) play for ?
2Finde∈ε:(player),plays-position,e)is truewhat position does (player) play ?
3Find e ∈ε:(player),is-aged,e) is truehow old is (player) ?what is the age of (player) ?
4Finde∈ε:(player),wears_number,e) is truewhat is the jersey number of (player) ?what number does (player) wear ?
5Finde ∈ε:(player),plays_for_country,e) is truewhat is the nationality of (player) ?which national team does (player) play for ?which country is (player) from ?
6Finde∈ε:(club),is-in_country,e)is truewhich country is the soccer team (club) based in ?
7Finde ∈ε: (club),plays_in_club-1,e)is truename a player from (club) ?who plays at the soccer club (club) ?who is from the professional football team (club) ?who plays professionally at (club) ?
8Finde ∈ε:(country-1),plays_for-country-1,e)is truewhich player is from (country_1) ?name a player from (country-1) ?who is from (country-1) ?who plays for the (country_1) national football team ?
9Finde∈ε:(position),playsposition-,e)is truename a player who plays (position) ?who plays (position) ?
10Finde ∈ε:(cotry-1),sicountry-1,e)is truewhich soccer club is based in (country_1) ?name a soccer club in (country_1) ?
11Finde∈ε:(player),plays_in_club /is_in_country,e)is truewhich country does (player) play professionally in ?where is the football club that (player) plays for ?
12Finde ∈ε:(country-1),plays-for-country-1/plays_in_club,e)is truewhich professional football team do players from (country_1) play for ？name a soccer club that has a player from (country_1) ?which professional football team has a player from (country_1) ?
13Find e∈ ε:(position),plays-position-1,e) is true and((club),plays-in_club-1,e) is truewho plays (position) for (club)?who are the (position) at (club) ?name a (position) that plays for (club) ?
14Find e∈ε: (position),plays-position-1,e) is true and(country-l),plays-for-country-1,e)is truewho plays (position) for (country_1) ?who are the (position) on (country_1) national team ?name a (position) from (country-1) ?which (country_2) footballer plays (position) ?name a (country-2) (position) ?
15Find e∈ε:(club)， plays_in_club-1,e) is true and(country_l),plays_for_country-1,e)is truewho are the (country_2) playersat (club)？which (country_2) footballer plays for (club) ?name a (country_2) player at (club) ?which player in (club) is from (country-1) ?
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#entity# atomic relations# atomic triplets112763977
#relations (atomic and compositional) in path queries# question and answer pairs in path queries(train/validation/ test）125620/804/1579
# types of questions in conjunctive queries# question and answer pairs in conjunctive queries(train/validation/test )31564/224/420
size of vocabulary1781
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SubjectRelationObject
david_villaplays-for_countryspain
lionel_messiplays_in-clubfc_barcelona
antoine-griezmannplays-positionforward
cristiano_ronaldowears_number7
fulham_fcis_in_countryengland
lukas_podolskiis_aged29
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#RelationTypeSample questionSample answer
1plays_in_clubmany-to-onewhich club doesalan pulido play for ?which professional footbal team does klaas jan huntelar play for ?tigres_uanlfc_schalke_04
2plays-positionmany-to-onewhat position does gonzalo higuain play ?ssc_napoli
3is_agedmany-to-onehow old is samuel etoo ?what is the age of luis suarez ?3
4wears-numbermany-to-onewhat is the jersey number of mario balotelli ?what number does shinji okazaki wear ?：
5plays_for_countrymany-to-onewhich country is thomas mueller from ?what is the nationality of helder postiga ?germanyportugal
6is.in_countrymany-to-onewhich country is the soccer team fc porto based in ?portugal
7plays_in_club-1one-to-manywho playsprofessionally at liverpool fc ?name a player from as roma ?steven_gerrardmiralem_pjanic
8plays-for_country-1one-to-manywhich player is from iran ？name a player from italy ?masoud_shojaeidaniele_de_rossi
9plays-position-1one-to-manyname a player who plays goalkeeper ?who plays forward ?gianluiqi-buffonraul_jimenez
10is_in-country-1one-to-manywhich soccer club is based in mexico ?name a soccer club in australia ?cruz_azul.fcmelbourne_victory_fc
11plays_in_club /is_in_countrymany-to-onewhere is the club that edin dzeko plays for ?which country does sime vrsaljko play professionally in ?englanditaly
12plays-for_country-1/plays_in_clubmany-to-manyname a soccer club that has a player from australia?name a soccer club that has a player from spain ?crystal_palace_fcfc_barcelona
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#RelationsSample questionsEntities in questionsSampleanswer
13plays_position-1 and plays_in_club-1who plays forward for fc barcelona ? who are the midfielders at fc bayern muenchen ?forward,fc_barcelona midfielder,fc_bayern_muenchenlionel_messi toni_kroos
14plays-position -1 andwho are the defenders on german national team ? which mexican footballer plays forward ?defender,germany defender,mexicoper_mertesacker raul-jimenez
15plays_in_club-1 and plays_for_country -1which player in paris saint-germain fc is from argentina ? who are the korean players at beijing guoan ?paris_saint-germain_fc,argentina beijing-guoan,koreaezequiel_lavezzi ha-daesung
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TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#RelationH@1(%)Mean Filtered RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered RankH@1(%)Mean Filtered Rank
1plays.in.club75.541.3893.481.0999.861.0098.511.02
2plays-position96.331.0494.021.0998.371.02100.001.00
3is_aged55.031.6991.441.1296.881.03100.001.00
4wears_number38.862.0978.671.3295.921.04100.001.00
5plays_for_country71.601.3994.841.1099.321.01100.001.00
6is_in_country98.321.0399.661.0099.331.01100.001.00
7plays_in_club-187.501.4683.421.4594.701.0797.421.03
882.471.6868.213.3725.275.6698.781.02
9plays-position-1100.001.0075.541.6013.5924.3598.781.02
10is_in-country-123.1126.9223.4823.278.32130.5919.4183.61
11plays_in_club/is_in-country20.247.0558.291.9846.882.9980.161.38
12plays-for_country -1/plays-in_club25.3222.2727.7310.0419.0435.5920.1533.01
Overall(Path relations) plays-position-164.645.0975.023.5967.2214.8786.738.79
13and plays-in_club-1 plays-position91.851.2069.971.8277.451.8395.381.06
14and plays_in_club =T91.711.2366.712.8551.494.8897.831.05
15and is_in_country -188.591.2073.37 70.021.80 2.1683.421.3494.701.08
Overall (Conj.relations)90.721.2170.792.6895.971.06
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TransE (SINGLE)TransE (COMP)TransGaussian (SINGLE)TransGaussian (COMP)
#Relation and sample questionMean H@1(%）Filtered RankH@1(%)Mean Filtered RankMean H@1(%) Filtered RankH@1(%)Mean Filtered Rank
1plays.in_club (which club does alan pulido play for?)90.60 1.1292.621.1196.64 1.0397.991.03
2plays-position (what position does gonzalo higuain play?)100.00 1.0098.111.0298.74 1.01100.001.00
3is_aged (how old is samuel etoo?)81.58 1.3092.111.1096.05 1.04100.001.00
4wears_number (what is the jersey number of mario balotelli?)44.29 1.8885.711.1996.43 1.04100.001.00
5plays-for-country (which country is thomas mueller from ?)97.60 1.0294.401.1198.40 1.0299.201.01
6is_in.country (which country is the soccer team fc porto based in ?)98.48 1.0298.481.0293.94 1.0898.481.02
7plays_in_club-1 (who plays professionally at liverpool fc?)95.12 1.0886.991.3896.75 1.0396.751.03
8plays_for_country (which player is from iran?)81.16 1.6172.462.3640.58 3.1993.241.48
9plays-position (name a player who plays goalkeeper?)100.00 1.0030.212.3055.21 5.0985.421.15
10is.in_country (which soccer club is based in mexico?)24.58 11.4723.7310.075.08 9.1817.8020.10
11plays_in_club/is_in_country (where is the club that edin dzeko plays for ?)48.68 4.2462.502.0748.03 2.4176.971.50
12plays-for-country-1/plays-in-club (name a soccer club that hasaplayer from australia ?)34.78 9.4930.4311.266.52 9.8816.3020.27
Overall74.92 2.8074.352.7170.172.82 84.423.68
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TransE(SINGLE)TransE(COMP)TransGaussian(SINGLE)TransGaussian(COMP)
#Relation and sample questionMeanH@1(%)FilteredRankMeanH@1(%)FilteredRankMeanH@1(%)FilteredRankMeanH@1(%)FilteredRank
13(who plays forward for fc barcelona?)94.48 1.1071.17 1.7787.12 1.3798.77 1.02
14plays-position-and plays-for-country-1(who are the defenders on german national team?)95.93 1.0876.42 2.5064.23 2.02100.00 1.00
15plays_in_club-1andis_in_country(which player in ssc napoli is from argentina?)91.79 1.1375.37 1.7588.06 1.3794.03 1.07
Overall94.05 1.1174.05 1.9780.71 1.5697.62 1.03
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ModelAccuracy (%)
TransE (SINGLE)68.5
TransE (COMP)80.3
TransGaussian (SINGLE)58.4
TransGaussian (COMP)76.4
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This improves robustness significantly as measured by unaligned duration ratio and word deletion rate, two metrics introduced in this paper for large-scale robustness evaluation using a pre-trained speech recognition model. With the use of Gaussian upsampling, Non-Attentive Tacotron achieves a 5-scale mean opinion score for naturalness of 4.41, slightly outperforming Tacotron 2. The duration predictor enables both utterance-wide and per-phoneme control of duration at inference time. When accurate target durations are scarce or unavailable in the training data, we propose a method using a fine-grained variational auto-encoder to train the duration predictor in a semi-supervised or unsupervised manner, with results almost as good as supervised training. + +# 1 INTRODUCTION + +Autoregressive neural text-to-speech (TTS) models using an attention mechanism are known to be able to generate speech with naturalness on par with recorded human speech. However, these types of models are known to be less robust than traditional approaches (He et al., 2019; Zheng et al., 2019; Guo et al., 2019; Battenberg et al., 2020). These autoregressive networks that predict the output one frame at a time are trained to decide whether to stop at each frame, and thus a misprediction on a single frame can result in serious failures such as early cut-off. Meanwhile, there are little to no hard constraints imposed on the attention mechanism to prevent problems such as repetition, skipping, long pause or babbling. To exacerbate the issue, these failures are rare and are thus often not represented in small test sets, such as those used in subjective listening tests. However, in customer-facing products, even a one-in-a-million chance of such problems can severely degrade the user experience. + +There have been various works aimed at improving the robustness of autoregressive attention-based neural TTS models. Some of them investigated reducing the effect of the exposure bias on the autoregressive decoder, using adversarial training (Guo et al., 2019) or adding regularization to encourage the forward and backward attention to be consistent (Zheng et al., 2019). Others utilized or designed alternative attention mechanisms, such as Gaussian mixture model (GMM) attention (Graves, 2013; Skerry-Ryan et al., 2018), forward attention (Zhang et al., 2018), stepwise monotonic attention (He et al., 2019), or dynamic convolution attention (Battenberg et al., 2020). Nonetheless, these approaches do not fundamentally solve the robustness issue. + +Recently, there has been a surge in the use of non-autoregressive models for TTS. Rather than predicting whether to stop on each frame, non-autoregressive models need to determine the output length ahead of time, and one way to do so is with an explicit prediction of the duration for each input token. A side benefit of such a duration predictor is that it is significantly more resilient to the failures afflicting the attention mechanism. + +However, one-to-many regression problems like TTS can benefit from an autoregressive decoder as the previous mel-spectrogram frames provides context to disambiguate between multi-modal outputs. + +In this paper, we propose, Non-Attentive Tacotron1, a neural TTS model that combines the robust duration predictor with the autoregressive decoder of Tacotron 2 (Shen et al., 2018). + +Our work is similar to DurIAN (Yu et al., 2019; Zhang et al., 2020), which incorporates the duration predictor with an autoregressive decoder. But besides the differences in architecture, we also introduce a couple of novel features in our model. + +The key contributions of this paper are summarized as follows: + +1. Replacing the attention mechanism in Tacotron 2 with duration prediction and upsampling modules leading to better robustness with the naturalness matching recorded natural speech; +2. Introduction of Gaussian upsampling significantly improving the naturalness compared to vanilla upsampling through repetition; +3. Global and fine-grained controlling of durations at inference time; +4. Semi-supervised and unsupervised duration modeling of Non-Attentive Tacotron, allowing the model to be trained with few to no duration annotations; and +5. More reliable evaluation metrics for measuring robustness of TTS models, as well as comparing Non-Attentive Tacotron with Tacotron 2 with respect to those metrics. + +# 2 RELATED WORKS + +In the past decade, model-based TTS synthesis has evolved from hidden Markov model (HMM)-based approaches (Zen et al., 2009) to using deep neural networks. Over this period, the concept of using an explicit representation of token (phoneme) durations has not been foreign. Early neural parametric synthesis models (Zen et al., 2013) require explicit alignments between input and target and include durations as part of the bag of features used to generate vocoder parameters. Explicit durations continue to be used with the advent of the end-to-end neural vocoder WaveNet (Oord et al., 2016) in works such as Deep Voice (Arik et al., 2017; Gibiansky et al., 2017) and CHiVE (Kenter et al., 2019). + +As general focus turned towards end-to-end approaches, the autoregressive sequence-to-sequence model with attention mechanism used in neural machine translation (NMT) (Bahdanau et al., 2015) and automatic speech recognition (ASR) (Chan et al., 2016) became an attractive option, removing the need to represent durations explicitly. This led to works such as Char2Wav (Sotelo et al., 2017), Tacotron (Wang et al., 2017; Shen et al., 2018), Deep Voice 3 (Ping et al., 2018), and Transformer TTS (Li et al., 2019). Similar models have been used for more complicated problems, like direct speech-to-speech translation (Jia et al., 2019), speech conversion (Biadsy et al., 2019), and speech enhancement (Ding et al., 2020). + +Tacotron 2, on which our work is based, is one such model. It connects a character-level encoder and an autoregressive decoder producing mel spectrogram frames with the use of a location-sensitive attention mechanism (Chorowski et al., 2015). + +Recently, there has been a surge of non-autoregressive models, bringing back the use of explicit duration prediction. This approach initially surfaced in NMT (Gu et al., 2017), then made its way into TTS with models such as FastSpeech (Ren et al., 2019; 2020), AlignTTS (Zeng et al., 2020), TalkNet (Beliaev et al., 2020), and JDI-T (Lim et al., 2020). See Appendix C for a rough categorization of these models. + +To train the duration predictor, FastSpeech uses target durations extracted from a pre-trained autoregressive model in teacher forcing mode, while JDI-T also extracts target durations from a separate autoregressive model but co-trains it with the feed-forward model. TalkNet uses a CTC-based ASR model to extract target durations, while CHiVE, FastSpeech 2, and DurIAN use target durations from an external aligner module utilizing forced alignment. Finally, AlignTTS forgoes target durations completely and uses a specialized alignment loss inspired by the Baum-Welch algorithm to train a mixture density network for alignment. + +![](images/ef6245d28d6e5fe72286aed10af02936b934c22bae4b4a6aeddb69c0fa845c3b.jpg) +Figure 1: Architecture of Non-Attentive Tacotron. + +# 3 MODEL + +Modern neural TTS models typically consist of two separate networks: (1) a feature generation network that transforms input tokens (e.g., grapheme or phoneme ids) into acoustic features (e.g., mel-spectrogram), and (2) a vocoder network that transforms the acoustic features into a time-domain audio waveform. This paper focuses on the feature generation network, and can be used with any vocoder network, e.g., WaveNet (Oord et al., 2016), WaveRNN (Kalchbrenner et al., 2018), WaveGlow (Prenger et al., 2019), MelGAN (Kumar et al., 2019), or WaveGrad (Chen et al., 2020). The architecture of Non-Attentive Tacotron is illustrated in Figure 1a. See Appendix A for specific parameter value settings. + +The model follows that of Tacotron 2 (Shen et al., 2018), transforming input ids $\pmb { X } = ( \pmb { x } _ { 1 } , \dots , \pmb { x } _ { N } )$ of length $N$ into mel-spectrogram predictions $\pmb { Y } = ( \pmb { y } _ { 1 } , \dots , \pmb { y } _ { T } )$ of size $T \times K$ . Phonemes are used as inputs, and include a silence token at word boundaries as well as an end-of-sequence token. The ids are used to index into a learned embedding and is then passed through an encoder consisting of 3 $\times$ (dropout, batch normalization, convolution) layers followed by a single bi-directional LSTM with ZoneOut to generate a 2-dimensional output of length $N$ . This output is concatenated with a speaker embedding vector to produce the final encoder output $\pmb { H } = ( h _ { 1 } , . . . , h _ { N } )$ . + +The autoregressive decoder also follows Tacotron 2, and predicts mel-spectrograms one frame at a time. At training time, teacher forcing (Williams & Zipser, 1989) is employed and the previous groundtruth mel-spectrogram frame is used as input, while at inference time the previous predicted mel-spectrogram frame is used. This previous frame is passed through a pre-net containing two fully-connected layers of ReLU units with dropout, then concatenated with an upsampled (aligned) encoder output corresponding to the current frame. The upsampled encoder outputs for future frames are not visible to the decoder at the current frame. In Tacotron 2, this upsampling or alignment is achieved using a location-sensitive attention mechanism (Chorowski et al., 2015), while in this work the attention mechanism is not used and a separate upsampling mechanism described later is used in its stead. The result is then passed through two uni-directional LSTM layers with ZoneOut. The LSTM output is concatenated with the upsampled encoder output yet again then projected to the mel-spectrogram dimension as frames of a preliminary predicted spectrogram $\mathbf { { \mathbf { { \mathbf { Y } } ^ { \prime } } } }$ . Once all the mel-spectrogram frames have been predicted, they are passed through a 5-layer batch normalized convolutional post-net with tanh activation on all except the last layer. The post-net predicts a residual to add to the prediction $\mathbf { { \mathbf { { \mathbf { Y } } ^ { \prime } } } }$ to obtain the final prediction $\mathbf { Y }$ . + +In place of the attention mechanism used in Tacotron 2, duration-based models upsample the encoder outputs using per-token duration information. This can be done by simply repeating each encoder output by its duration as in FastSpeech (Ren et al., 2019), but instead we adopt a different process we call Gaussian upsampling, which is described in subsection 3.1. Note that while durations in seconds are used for loss computation, they are converted to durations in integer frames for upsampling. + +For Gaussian upsampling, a duration and a range parameter must be predicted for each token. The range parameter is called thus because it controls the range of a token’s influence. The duration predictor passes the encoder output through two bi-directional LSTM layers followed by a projection layer to predict the numeric duration $\pmb { d } \overset { - } { = } ( d _ { 1 } , \ldots , d _ { N } )$ for each input token. During training, these predicted durations are only used for loss computation, and the target durations are used instead in the upcoming steps2. The range parameter predictor passes the encoder output concatenated with durations through two bi-directional LSTM layers followed by a projection layer and a SoftPlus activation to predict a positive range parameter $\sigma$ for each input token. + +After the encoder outputs are upsampled, a Transformer-style sinusoidal positional embedding (Vaswani et al., 2017) is concatenated. The positional embedding tracks the index of each upsampled frame within each token; if the duration values are [2, 1, 3], the indices for the positional embedding would be $[ 1 , 2 , 1 , 1 , 2 , 3 ]$ . + +The model is trained using a combination of duration prediction loss and mel-spectrogram reconstruction loss. The duration prediction loss is the $L ^ { 2 }$ loss between predicted and target durations in seconds, and the mel-spectrogram reconstruction loss is a $L ^ { 1 } + L ^ { 2 }$ loss between the predicted and the groundtruth mel-spectrogram both before and after the post-net (following Jia et al. (2018)). + +$$ +\begin{array} { r l r } { { \mathcal { L } = \mathcal { L } _ { \mathrm { s p e c } } + \lambda _ { \mathrm { d u r } } \mathcal { L } _ { \mathrm { d u r } } } } \\ & { } & { \mathcal { L } _ { \mathrm { d u r } } = \frac { 1 } { N } \| d - d ^ { * } \| _ { 2 } ^ { 2 } } \\ & { } & { \mathcal { L } _ { \mathrm { s p e c } } = \frac { 1 } { T K } \displaystyle \sum _ { t = 1 } ^ { T } \Big ( \| y _ { t } ^ { \prime } - y _ { t } ^ { * } \| _ { 1 } + \| y _ { t } ^ { \prime } - y _ { t } ^ { * } \| _ { 2 } ^ { 2 } + \| y _ { t } - y _ { t } ^ { * } \| _ { 1 } + \| y _ { t } - y _ { t } ^ { * } \| _ { 2 } ^ { 2 } \Big ) } \end{array} +$$ + +# 3.1 GAUSSIAN UPSAMPLING + +Given a sequence of vectors to be upsampled $\pmb { H } = ( h _ { 1 } , \ldots , h _ { N } )$ , integer duration values ${ \pmb d } =$ $( d _ { 1 } , \ldots , d _ { N } )$ , and range parameter values ${ \pmb \sigma } = ( \sigma _ { 1 } , \ldots , \sigma _ { N } )$ , we compute the upsampled vector sequence $U = ( \pmb { u } _ { 1 } , \dots , \pmb { u } _ { T } )$ as: + +$$ +c _ { i } = \frac { d _ { i } } { 2 } + \sum _ { j = 1 } ^ { i - 1 } d _ { j } , \qquad w _ { t i } = \frac { N \left( t ; c _ { i } , \sigma _ { i } ^ { 2 } \right) } { \sum _ { j = 1 } ^ { N } \mathcal { N } \left( t ; c _ { j } , \sigma _ { j } ^ { 2 } \right) } , \qquad \quad u _ { t } = \sum _ { i = 1 } ^ { N } w _ { t i } h _ { i } +$$ + +That is, we place a Gaussian distribution with standard deviation $\sigma _ { i }$ at the center of the output segment corresponding to the $i$ -th input token as determined by the duration values $^ d$ , and for each frame we take a weighted sum of the encoder outputs in accordance with the values of Gaussian distributions at that frame. This is similar to the softmax-based aligner in Donahue et al. (2020), except a learned $\pmb { \sigma }$ rather than a fixed temperature hyperparameter is used here. + +Compared with vanilla upsampling by repetition (as in Ren et al. (2019)), which can be seen as a case of learning a hard monotonic attention, Gaussian upsampling results in an alignment that is more akin to single-component GMM attention. Another benefit of Gaussian upsampling is that it is fully differentiable, which is critical to semi-supervised and unsupervised duration modeling (section 4) as it allows the gradients from the spectrogram losses to flow through to the duration predictor. + +# 3.2 TARGET DURATIONS + +Neural TTS models using duration need alignments between input tokens and output features. This can be accomplished by implementing an aligner module in the model or by using an external aligner. + +In our work, target durations are extracted by an external, flatstart trained, speaker-dependent HMMbased aligner with a lexicon (Talkin & Wightman, 1994). However, sometimes it is difficult to train a reliable aligner model and/or extract accurate alignments due to data sparsity, poor recording conditions, or unclear pronunciations. To address this problem, we introduce semi-supervised and unsupervised duration modeling. + +# 4 SEMI-SUPERVISED AND UNSUPERVISED DURATION MODELING + +A na¨ıve approach to unsupervised duration modeling would be to simply train the model using the predicted durations (instead of the target durations) for upsampling, and use only mel-spectrogram reconstruction loss for optimization. To match the length between the predicted durations and the target mel-spectrogram frames, the predicted per-token durations can be scaled by $T / \sum _ { i } d _ { i }$ . In addition to that, an utterance-level duration loss $\begin{array} { r } { \mathcal { L } _ { \mathrm { u } } = \frac { 1 } { N } \left( T - \sum _ { i } d _ { i } \right) ^ { 2 } } \end{array}$ could be added to the total loss. However, experiments show that such an approach does not produce satisfying naturalness in the synthesized speech (subsection 6.3). + +The proposed unsupervised duration modeling is illustrated in Figure 1b. We instead utilize a fine-grained VAE (FVAE) similar to Sun et al. (2020) to model the alignment between the input tokens and the target mel-spectrogram frames, and extract per-token latent features from the target mel-spectrogram based on this alignment. The token encoder output $\pmb { H }$ is aligned to the target spectrogram $Y ^ { * }$ using an attention mechanism following Lee & Kim (2019): + +$$ +\begin{array} { r } { \pmb { c } _ { i } = \mathrm { A t t n } ( \pmb { h } _ { i } , f _ { \mathrm { s p e c } } ( \pmb { Y } ^ { * } ) ) , } \end{array} +$$ + +where $\boldsymbol { h } _ { i }$ is used as the query in the attention, and $f _ { \mathrm { s p e c } }$ is a spectrogram encoder whose output per frame is used as the values in the attention. A simple dot-product attention from Luong et al. (2015) was used in this work. A latent feature $z _ { i }$ is then computed from $c _ { i }$ and $\boldsymbol { h } _ { i }$ using a variational auto-encoder (VAE) (Kingma & Welling, 2014) with a Gaussian prior $\mathcal { N } ( \mathbf { 0 } , \mathbf { I } )$ , optimized through the evidence lower bound (ELBO): + +$$ +\log p \left( { Y } \mid { H } \right) \geq - \sum _ { i } D _ { \mathrm { K L } } \left( q \left( \boldsymbol { z } _ { i } \mid h _ { i } , \boldsymbol { c } _ { i } \right) \parallel p \left( \boldsymbol { z } _ { i } \right) \right) + \mathbb { E } _ { q \left( \boldsymbol { z } _ { i } \mid h _ { i } , \boldsymbol { c } _ { i } \right) } \left[ \log p \left( { Y } \mid { H } , \boldsymbol { Z } \right) \right] +$$ + +where the first term is the KL divergence between the prior and posterior, and the second term can be approximated by drawing samples from the posterior. + +Because these latent features are extracted from the target spectrogram with an alignment, they are capable of carrying duration related information. At training time, the per-token duration $^ d$ is predicted from the concatenation of the token encoder output $\pmb { H }$ and the posterior latent $z$ ; while at inference time, the prior latent is used for $z$ (either sampled from the distribution or using the distribution mode), and the internal attention mechanism of the FVAE is not used. + +Unlike Sun et al. (2020), scheduled sampling was not utilized for factorizing latent dimensions. These latent features are only used for duration prediction, and are not used for range parameter prediction or mel-spectrogram reconstruction. We also cap the range parameters for each token to twice its predicted duration in this setup for better training stability. As in section 3, durations predicted in seconds are used for loss computation, but are converted to durations in integer frames for upsampling. + +The overall loss used for semi-supervised and unsupervised training is thus + +$$ +\mathcal { L } = \mathcal { L } _ { \mathrm { s p e c } } + \lambda _ { \mathrm { d u r } } \mathcal { L } _ { \mathrm { d u r } } + \lambda _ { \mathrm { u } } \mathcal { L } _ { \mathrm { u } } + \lambda _ { \mathrm { K L } } D _ { \mathrm { K L } } , +$$ + +where $D _ { \mathrm { K L } }$ and $\mathcal { L } _ { \mathrm { s p e c } }$ correspond to the first and second terms in Equation 4, respectively, and ${ \mathcal { L } } _ { \mathrm { d u r } }$ is only counted for examples with target duration labels (i.e. supervised examples). The last three terms are all weighted per valid token. + +# 5 ROBUSTNESS EVALUATION + +Previous work typically evaluated the robustness of TTS systems on a small set of handpicked “hard cases” (He et al., 2019; Zheng et al., 2019; Guo et al., 2019). Although such evaluation is helpful for guiding improvements, it is not reflective of the overall robustness of the system. The handpicked samples may be biased to the weaknesses of a certain system, and is prone to lead further optimization to overfit to the specific evaluation set. + +In this work, we evaluate the robustness of TTS systems on large evaluation sets in an automated way by leveraging existing ASR systems. We run ASR and forced alignment evaluations on the synthesized speech against the verbalized text, and report two metrics measuring over- and under-generation: + +1. Unaligned duration ratio (UDR): The synthesized speech is forced aligned with the verbalized input text using an ASR system. Each token in the input text is aligned to a segment in the synthesized audio. Any long audio segments $> 1$ second) not aligned to any input token are typically due to over-generation from the TTS system, such as long pauses, babbling, word repetitions, or failures to stop after finishing the utterance. The total duration of such long unaligned segments divided by the total output duration is the UDR. Note that short unaligned segments are ignored. If the synthesized speech is unable to be aligned with the input text, it is considered as having a UDR of $100 \%$ . +2. ASR word deletion rate (WDR): This is the deletion error portion in a standard ASR word error rate (WER) evaluation. Under-generation in the synthesized speech, such as early cutoff and word skipping, is reflected by a higher WDR. + +As the ASR system will make mistakes, the metrics above are just an upper-bound on the actual failures of the TTS system. + +# 6 EXPERIMENTS + +All models were trained on a proprietary dataset with 66 speakers with 4 different English accents (US, British, Australian, and Nigerian). The amount of data per speaker varied from merely 5 seconds to 47 hours, totaling 354 hours. + +A preliminary experiment comparing different attention mechanisms (including monotonic, stepwise monotonic, dynamic convolution and GMM attention (GMMA)) showed that GMMA performed the best. We therefore compared our non-attentive Tacotron not only with Tacotron 2 with locationsensitive attention (LSA) which was used in the original Tacotron 2 paper but also with Tacotron 2 with GMMA. The Tacotron 2 models used reduction factor 2 and $L ^ { 1 } + L ^ { 2 }$ loss. + +Following Shen et al. (2018), predicted features were obtained in teacher-forcing mode from a Tacotron 2 model and used to train a WaveRNN vocoder which was then used for all experiments. + +# 6.1 NATURALNESS + +The naturalness of the synthesized speech was evaluated through subjective listening tests, including 5-scale Mean Opinion Score (MOS) tests and side-by-side preference tests. The sentences were synthesized using 10 US English speakers (5 male / 5 female) in a round-robin fashion. The amount of training data for the evaluated speakers varied from 3 hours to 47 hours. + +Table 1 contains MOS results. Non-Attentive Tacotron with Gaussian upsampling matched Tacotron 2 (GMMA) in naturalness, and both were close to the groundtruth audio. A preference test between + +Table 1: MOS with $9 5 \%$ confidence intervals. + +
ModelMOS
Tacotron 2
w/LSA4.35 ± 0.05
w/ GMMA4.37 ± 0.04
Non-Attentive Tacotron w/ Gauss. upsampling
w/ vanilla upsampling4.41 ± 0.04
4.13 ± 0.05
Ground truth4.42 ± 0.04
+ +![](images/298c40f45176871a5c45d749a449e03d55efe7148d2e82ce9a206d5b085a6fcd.jpg) +Figure 2: Preference test result with Non-Attentive Tacotron with Gaussian upsampling compared against Tacotron 2 (GMMA). + +Non-Attentive Tacotron and Tacotron 2 (GMMA) further confirmed this result, as shown in Figure 2. Non-Attentive Tacotron with vanilla (repeating) upsampling was rated as significantly less natural than with Gaussian upsampling. + +The effectiveness of a learned range parameter versus a fixed temperature hyperparameter set at 10.0 as per Donahue et al. (2020) is compared using a preference test in Table 2. While there is only a slight perceived benefit in using a learned range parameter, it reduces the need to tune another dataset-dependent hyperparameter. Additionally, in multi-speaker setups it is possible that the optimal $\sigma$ may be speaker-dependent. + +Table 2: Preference test between a learned $\sigma$ versus a fixed $\sigma$ set at 10.0. Pace is defined as in subsection 6.2. A negative preference value means that the learned $\sigma$ is preferred over the fixed $\sigma$ . + +
Pace0.8×1.0×1.25×
Preference -0.017 ±0.057 -0.055±0.054 -0.017±0.055
+ +# 6.2 PACE CONTROL + +Table 3 shows WER and MOS results after modifying the utterance-wide pace by dividing the predicted durations by various factors. The WER is computed on speech synthesized on transcripts from the LibriTTS test-clean subset with the same 10 speakers in subsection 6.1, and then transcribed by an ASR model described in Park et al. (2020) with a WER of $2 . 3 \%$ on the ground truth audio. + +With pace between $0 . 8 \times - 1 . 2 5 \times$ , the WERs were hardly impacted. The WER was significantly worse when the pace was increased to $1 . 5 \times$ normal, partially because the ASR model used was not optimized for speech so fast. In contrast, the subjective MOS decreased rapidly when the pace was sped up or slowed down significantly. However, most of the comments from raters were simply complaining about the pace, such as “too slow to be natural” $\mathbf { \eta } ^ { ( 0 . 8 \mathbf { x } ) }$ or “way too fast” $( 1 . 2 5 \mathrm { x } )$ . + +Non-Attentive Tacotron is also able to control the pace of the synthesized speech at a finer granularity, such as per-word or per-phoneme, while still maintain the naturalness of the synthesized speech. Figure 3 shows examples of controlling the pace for specific words in a sentence. + +![](images/258a479afa848b55bc11081ce643fbccc1c6df42fb7881e28e3ba4917dd524cd.jpg) +Figure 3: Single word pace control with sentence “I’m so saddened about the devastation in Big Basin.” The top spectrogram is with regular pace. The rest slow down the words “saddened”, “devastation”, and “Big Basin” respectively to $0 . 6 7 \times$ the regular pace by scaling the predicted duration by $1 . 5 \times$ . + +Table 3: Performance of controlling the utterance-wide pace of the synthesized speech. + +
Pace0.67×0.8×0.9×1.0×1.11×1.25×1.5×
WER3.3%2.8%2.6%2.6%2.5%2.7%6.1%
MOS3.28 ± 0.063.87 ± 0.054.24 ± 0.044.41 ± 0.044.28 ± 0.043.79 ± 0.063.18± 0.06
+ +# 6.3 SEMI-SUPERVISED AND UNSUPERVISED DURATION MODELING + +Ten different US English speakers (5 male / 5 female) each with about 4 hours of training data were used for evaluating the performance of the unsupervised and semi-supervised duration modeling. + +![](images/26daa5ffb38bf9f1cab4ee35f8b59eb8c80db08b72734cb992f60f581080fb60.jpg) +Figure 4: Alignment on text “What time do I need to show up to my sky diving lesson?” from the unsupervised model. The predicted alignments are from Gaussian upsampling. + +Table 4: Performance of unsupervised and semi-supervised duration modeling. Zero vectors are used as FVAE latents for inference. MAE denotes the mean absolute error. + +
TrainingModelDur. MAE (ms)MOS
Unsupervisedw/o FVAE124.42.91± 0.09
w/ FVAE41.34.31 ± 0.04
Semi-supervisedw/o FVAE21.54.19 ± 0.05
Supervisedw/FVAE18.34.35 ± 0.04
Non-Attentive Tacotron15.44.37 ± 0.04
Tacotron2 w/ GMMA-4.35 ± 0.04
Ground truth=4.52 ± 0.03
+ +The duration labels for these 10 speakers (i.e. about $11 \%$ of the training data) were withheld for the semi-supervised models, and all duration labels were withheld for the unsupervised models. + +Figure 4 shows predicted alignment after Gaussian upsampling and the internal alignment from the attention module in the FVAE compared with the alignment computed from the target durations, for the unsupervised model. Despite not having access to any target durations, both the FVAE and duration predictor were able to produce an alignment close to that computed from the target durations. + +As shown in Table 4, with the use of the FVAE, the naturalness of both semi-supervised and unsupervised models were very close to that of the supervised models, even though duration prediction errors were higher. The autoregressive decoder trained with teacher forcing may have been powerful enough to correct the duration prediction errors to some degree. However, the naturalness degraded significantly without the use of the FVAE. Although the duration error from the semi-supervised model without FVAE was lower than that from the unsupervised model with FVAE, the former was significantly less natural than the latter. This may be due to a lower consistency between supervised and unsupervised speakers without FVAE. + +Although these models were close to the supervised model in MOS, manual investigation found that samples from both semi-supervised models and unsupervised models had a small chance of containing slight errors that do not occur in the supervised model, such as unclear pronunciations, phoneme repetitions, or extra pauses. However, they are significantly less severe than similar errors from Tacotron 2, mostly impacting just one or a few phonemes. These errors are further confirmed in the large scale robustness evaluation (subsection 6.4). + +The utterance-wide or fine-grained pace control (subsection 6.2) can be applied to the semi-supervised and unsupervised models as well. However, as the alignments are not as accurate, the synthesized speech with fine-grained pace control are not as natural as from the supervised model. The duration may be extended by simply inserting more silence, and the extended portion may include phoneme repetitions or unclear pronunciations. + +Table 5: Robustness measured by UDR and WDR on two large evaluation sets. The evaluation speakers are unsupervised ones in the semi-supervised and unsupervised models. + +
SystemLibriTTSweb-long
UDR (%)WDR (%)UDR (%)WDR (%)
Tacotron 2
w/LSA16.960.446.044.4
w/ GMMA3.8120.16.1571.3
Non-Attentive Tacotron
Supervised0.0050.10.0111.1
Semi-supervised0.2660.90.6953.5
Unsupervised0.2230.70.5273.2
+ +# 6.4 ROBUSTNESS + +We evaluated the robustness of the neural TTS models by measuring UDR and WDR on two large evaluation sets: LibriTTS: 354K sentences from all train subsets from the LibriTTS corpus (Zen et al., 2019); and web-long: 100K long sentences mined from the web, which included a small amount of irregular text such as programming code. The median text lengths of the two sets were 74 and 224 characters, respectively. The input was synthesized using the same 10 speakers in subsection 6.3 in a round-robin fashion. All model outputs were capped at 120 seconds. + +We used the ASR model trained on the LibriSpeech (Panayotov et al., 2015) and LibriLight (Kahn et al., 2020) corpora from Park et al. (2020) for measuring WDR, and a confidence islands-based forced alignment model (Chiu et al., 2018) for measuring UDR. + +Table 5 shows the robustness metrics for Tacotron 2 and Non-Attentive Tacotron. Tacotron 2 (LSA) suffered from severe over-generation as measured by UDR, especially on long inputs. Manual investigation uncovered that they were typically long babbling or long silence, often at the end (failure to stop). It also had a high level of under-generation as measured by WDR, typically due to early cutoff. Tacotron 2 (GMMA) performed almost as well as the supervised Non-Attentive Tacotron in WDR because of its soft monotonic nature, which made end-of-sentence prediction easier. However, it still had significantly higher level of over-generation compared to Non-Attentive Tacotron, even when unsupervised or semi-supervised duration modeling is used for the latter. The robustness of semi-supervised and unsupervised Non-Attentive Tacotron is significantly worse than the supervised one. Manual investigation uncovered that the typical failure pattern is that part of the spectrogram is not correctly synthesized (often as silence, but sometimes as babbling), despite that the duration prediction seems reasonable. Such failure pattern contributes to both UDR and WDR. This indicates further improvements to be made. Even then, the semi-supervised and unsupervised Non-Attentive Tacotron still performs significantly better on over-generation compared to Tacotron 2. + +In practice, we also observed that Tacotron 2 required significantly more care in data preprocessing to achieve this level of robustness, including consistent trimming of leading and trailing silences and filtering out utterances with long pauses. On the other hand, Non-Attentive Tacotron is significantly less sensitive to the data preprocessing steps. + +# 7 CONCLUSIONS + +This paper presented Non-Attentive Tacotron, showing a significant improvement in robustness compared to Tacotron 2 as measured by unaligned duration ratio and word deletion rate, while also slightly outperforming it in naturalness. This was achieved by replacing the attention mechanism in Tacotron 2 with an explicit duration predictor and Gaussian upsampling. We demonstrated the ability to control the pacing of the entire utterance as well as individual words using the duration predictor. 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CommonTraining modeSynchronous 32
Batch size (per replica) Replicas Parameter init L² regularization Learning rate Learning rate scheduleXavier 1 ×10-6 0.001
Inputs and TargetsOptimizer LSTM zone-out prob LSTM cell abs value cap Sampling rate (Hz) Normalize waveform Pre-emphasis Frame size (ms) Frame hop (ms)decay half every 50K steps. Adam(0.9,0.999,1 × 10-6) 0.1 10.0 24,000 No No 50
EncoderMel channels K Mel frequency lower bound (Hz) Mel frequency upper bound (Hz)128 20 12,000
FVAE
Yes
512×2
5×1
512 64
Mel spectrogram dynamic range compressionlog(x +0.001)
Token embedding dim
Speaker embedding dim
Conv kernel
Conv dim[512, 512, 512]
Conv activation[None,None,None]
Conv batch norm decay0.999
Bi-LSTM dim
Segment encoder conv kernel3×1
Segment encoder conv dim[512,512,512]
Segment encoder Bi-LSTM dim256×2
Layer norm attention inputs
Latent dim8 projected to 16
Duration PredictorBi-LSTM dim512×2
Projection activationNone
Xdur supervised2.0
Xdur semi-supervised100.0
100.0
Au semi-supervised1×10-3
XKL semi-supervised
Xu unsupervised1.0
Range Parameter Predictor入KL unsupervised1 ×10-4
Bi-LSTM dim512×2
Positional EmbeddingProjection activationSoftPlus
Embedding dim32
Timestep denominator10.000
Decoder[256,256]
Pre-net dim supervised
Pre-net dim semi/unsupervised[128,128]
Pre-net activation[ReLU,ReLU]
[0.5,0.5]
Pre-net dropout prob
LSTM dim^1,024
LSTM inituniform(0.1)
Projection inituniform(0.1)
Post-net conv kernel5×1
Post-net conv dim
[512,512,512,512,128]
Post-net conv activation
[tanh,tanh,tanh,tanh,None]
Post-net conv init
+ +# B WER BREAKDOWNS IN THE ROBUSTNESS EVALUATION + +Table 7: WER breakdowns in the robustness evaluation. Deletion rate (del) is the WDR in Table 5. + +
SystemLibriTTSweb-long
WERdelinssubWERdelinssub
Tacotron 2
w/LSA1.80.40.31.113.04.42.06.7
w/ GMMA1.70.10.11.510.11.31.37.4
Non-Attentive Tacotron
Supervised1.40.10.11.29.31.11.36.9
Semi-supervised3.30.90.22.214.13.51.69.0
Unsupervised3.50.70.32.615.33.22.010.1
+ +# C CLASSIFICATION OF SOME TTS MODELS + +Table 8: Classification of some TTS models into autoregressive (AR)/feed-forward (FF), RNN/Transformer/fully convolutional, and attention-based/duration-based. + +
ModelYearARFFRNNTransformerFull ConvAttentionDuration
Deep Voice2017
Char2Wav2017
Tacotron2017
Deep Voice 22017
Tacotron 22018
Deep Voice 32018
Transformer TTS2019
CHiVE2019
DurIAN2019
Fastspeech2019
TalkNet2020
AlignTTS2020
JDI-T2020
Non-Attentive Tacotron2020
\ No newline at end of file diff --git a/parse/train/CGFN_nV1ql/CGFN_nV1ql_content_list.json b/parse/train/CGFN_nV1ql/CGFN_nV1ql_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..fa2d4eaedbdc1029298426de7c4fecba586c8863 --- /dev/null +++ b/parse/train/CGFN_nV1ql/CGFN_nV1ql_content_list.json @@ -0,0 +1,1714 @@ +[ + { + "type": "text", + "text": "NON-ATTENTIVE TACOTRON: ROBUST AND CONTROLLABLE NEURAL TTS SYNTHESIS INCLUDING UNSUPERVISED DURATION MODELING ", + "text_level": 1, + "bbox": [ + 176, + 98, + 790, + 172 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Anonymous authors Paper under double-blind review ", + "bbox": [ + 184, + 195, + 398, + 223 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 260, + 544, + 275 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper presents Non-Attentive Tacotron based on the Tacotron 2 text-to-speech model, replacing the attention mechanism with an explicit duration predictor. This improves robustness significantly as measured by unaligned duration ratio and word deletion rate, two metrics introduced in this paper for large-scale robustness evaluation using a pre-trained speech recognition model. With the use of Gaussian upsampling, Non-Attentive Tacotron achieves a 5-scale mean opinion score for naturalness of 4.41, slightly outperforming Tacotron 2. The duration predictor enables both utterance-wide and per-phoneme control of duration at inference time. When accurate target durations are scarce or unavailable in the training data, we propose a method using a fine-grained variational auto-encoder to train the duration predictor in a semi-supervised or unsupervised manner, with results almost as good as supervised training. ", + "bbox": [ + 233, + 300, + 766, + 467 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 515, + 336, + 531 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Autoregressive neural text-to-speech (TTS) models using an attention mechanism are known to be able to generate speech with naturalness on par with recorded human speech. However, these types of models are known to be less robust than traditional approaches (He et al., 2019; Zheng et al., 2019; Guo et al., 2019; Battenberg et al., 2020). These autoregressive networks that predict the output one frame at a time are trained to decide whether to stop at each frame, and thus a misprediction on a single frame can result in serious failures such as early cut-off. Meanwhile, there are little to no hard constraints imposed on the attention mechanism to prevent problems such as repetition, skipping, long pause or babbling. To exacerbate the issue, these failures are rare and are thus often not represented in small test sets, such as those used in subjective listening tests. However, in customer-facing products, even a one-in-a-million chance of such problems can severely degrade the user experience. ", + "bbox": [ + 174, + 554, + 825, + 693 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There have been various works aimed at improving the robustness of autoregressive attention-based neural TTS models. Some of them investigated reducing the effect of the exposure bias on the autoregressive decoder, using adversarial training (Guo et al., 2019) or adding regularization to encourage the forward and backward attention to be consistent (Zheng et al., 2019). Others utilized or designed alternative attention mechanisms, such as Gaussian mixture model (GMM) attention (Graves, 2013; Skerry-Ryan et al., 2018), forward attention (Zhang et al., 2018), stepwise monotonic attention (He et al., 2019), or dynamic convolution attention (Battenberg et al., 2020). Nonetheless, these approaches do not fundamentally solve the robustness issue. ", + "bbox": [ + 174, + 700, + 825, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, there has been a surge in the use of non-autoregressive models for TTS. Rather than predicting whether to stop on each frame, non-autoregressive models need to determine the output length ahead of time, and one way to do so is with an explicit prediction of the duration for each input token. A side benefit of such a duration predictor is that it is significantly more resilient to the failures afflicting the attention mechanism. ", + "bbox": [ + 176, + 819, + 823, + 888 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, one-to-many regression problems like TTS can benefit from an autoregressive decoder as the previous mel-spectrogram frames provides context to disambiguate between multi-modal outputs. ", + "bbox": [ + 174, + 895, + 823, + 922 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose, Non-Attentive Tacotron1, a neural TTS model that combines the robust duration predictor with the autoregressive decoder of Tacotron 2 (Shen et al., 2018). ", + "bbox": [ + 173, + 103, + 823, + 132 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work is similar to DurIAN (Yu et al., 2019; Zhang et al., 2020), which incorporates the duration predictor with an autoregressive decoder. But besides the differences in architecture, we also introduce a couple of novel features in our model. ", + "bbox": [ + 176, + 138, + 823, + 180 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The key contributions of this paper are summarized as follows: ", + "bbox": [ + 173, + 188, + 584, + 202 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1. Replacing the attention mechanism in Tacotron 2 with duration prediction and upsampling modules leading to better robustness with the naturalness matching recorded natural speech; \n2. Introduction of Gaussian upsampling significantly improving the naturalness compared to vanilla upsampling through repetition; \n3. Global and fine-grained controlling of durations at inference time; \n4. Semi-supervised and unsupervised duration modeling of Non-Attentive Tacotron, allowing the model to be trained with few to no duration annotations; and \n5. More reliable evaluation metrics for measuring robustness of TTS models, as well as comparing Non-Attentive Tacotron with Tacotron 2 with respect to those metrics. ", + "bbox": [ + 210, + 215, + 825, + 382 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 RELATED WORKS ", + "text_level": 1, + "bbox": [ + 176, + 409, + 354, + 424 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the past decade, model-based TTS synthesis has evolved from hidden Markov model (HMM)-based approaches (Zen et al., 2009) to using deep neural networks. Over this period, the concept of using an explicit representation of token (phoneme) durations has not been foreign. Early neural parametric synthesis models (Zen et al., 2013) require explicit alignments between input and target and include durations as part of the bag of features used to generate vocoder parameters. Explicit durations continue to be used with the advent of the end-to-end neural vocoder WaveNet (Oord et al., 2016) in works such as Deep Voice (Arik et al., 2017; Gibiansky et al., 2017) and CHiVE (Kenter et al., 2019). ", + "bbox": [ + 174, + 443, + 825, + 541 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As general focus turned towards end-to-end approaches, the autoregressive sequence-to-sequence model with attention mechanism used in neural machine translation (NMT) (Bahdanau et al., 2015) and automatic speech recognition (ASR) (Chan et al., 2016) became an attractive option, removing the need to represent durations explicitly. This led to works such as Char2Wav (Sotelo et al., 2017), Tacotron (Wang et al., 2017; Shen et al., 2018), Deep Voice 3 (Ping et al., 2018), and Transformer TTS (Li et al., 2019). Similar models have been used for more complicated problems, like direct speech-to-speech translation (Jia et al., 2019), speech conversion (Biadsy et al., 2019), and speech enhancement (Ding et al., 2020). ", + "bbox": [ + 174, + 547, + 825, + 660 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Tacotron 2, on which our work is based, is one such model. It connects a character-level encoder and an autoregressive decoder producing mel spectrogram frames with the use of a location-sensitive attention mechanism (Chorowski et al., 2015). ", + "bbox": [ + 176, + 666, + 821, + 708 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, there has been a surge of non-autoregressive models, bringing back the use of explicit duration prediction. This approach initially surfaced in NMT (Gu et al., 2017), then made its way into TTS with models such as FastSpeech (Ren et al., 2019; 2020), AlignTTS (Zeng et al., 2020), TalkNet (Beliaev et al., 2020), and JDI-T (Lim et al., 2020). See Appendix C for a rough categorization of these models. ", + "bbox": [ + 174, + 715, + 825, + 785 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To train the duration predictor, FastSpeech uses target durations extracted from a pre-trained autoregressive model in teacher forcing mode, while JDI-T also extracts target durations from a separate autoregressive model but co-trains it with the feed-forward model. TalkNet uses a CTC-based ASR model to extract target durations, while CHiVE, FastSpeech 2, and DurIAN use target durations from an external aligner module utilizing forced alignment. Finally, AlignTTS forgoes target durations completely and uses a specialized alignment loss inspired by the Baum-Welch algorithm to train a mixture density network for alignment. ", + "bbox": [ + 174, + 792, + 825, + 890 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ef6245d28d6e5fe72286aed10af02936b934c22bae4b4a6aeddb69c0fa845c3b.jpg", + "image_caption": [ + "Figure 1: Architecture of Non-Attentive Tacotron. " + ], + "image_footnote": [], + "bbox": [ + 220, + 102, + 813, + 397 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 MODEL ", + "text_level": 1, + "bbox": [ + 174, + 422, + 269, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Modern neural TTS models typically consist of two separate networks: (1) a feature generation network that transforms input tokens (e.g., grapheme or phoneme ids) into acoustic features (e.g., mel-spectrogram), and (2) a vocoder network that transforms the acoustic features into a time-domain audio waveform. This paper focuses on the feature generation network, and can be used with any vocoder network, e.g., WaveNet (Oord et al., 2016), WaveRNN (Kalchbrenner et al., 2018), WaveGlow (Prenger et al., 2019), MelGAN (Kumar et al., 2019), or WaveGrad (Chen et al., 2020). The architecture of Non-Attentive Tacotron is illustrated in Figure 1a. See Appendix A for specific parameter value settings. ", + "bbox": [ + 174, + 458, + 825, + 569 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The model follows that of Tacotron 2 (Shen et al., 2018), transforming input ids $\\pmb { X } = ( \\pmb { x } _ { 1 } , \\dots , \\pmb { x } _ { N } )$ of length $N$ into mel-spectrogram predictions $\\pmb { Y } = ( \\pmb { y } _ { 1 } , \\dots , \\pmb { y } _ { T } )$ of size $T \\times K$ . Phonemes are used as inputs, and include a silence token at word boundaries as well as an end-of-sequence token. The ids are used to index into a learned embedding and is then passed through an encoder consisting of 3 $\\times$ (dropout, batch normalization, convolution) layers followed by a single bi-directional LSTM with ZoneOut to generate a 2-dimensional output of length $N$ . This output is concatenated with a speaker embedding vector to produce the final encoder output $\\pmb { H } = ( h _ { 1 } , . . . , h _ { N } )$ . ", + "bbox": [ + 173, + 575, + 825, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The autoregressive decoder also follows Tacotron 2, and predicts mel-spectrograms one frame at a time. At training time, teacher forcing (Williams & Zipser, 1989) is employed and the previous groundtruth mel-spectrogram frame is used as input, while at inference time the previous predicted mel-spectrogram frame is used. This previous frame is passed through a pre-net containing two fully-connected layers of ReLU units with dropout, then concatenated with an upsampled (aligned) encoder output corresponding to the current frame. The upsampled encoder outputs for future frames are not visible to the decoder at the current frame. In Tacotron 2, this upsampling or alignment is achieved using a location-sensitive attention mechanism (Chorowski et al., 2015), while in this work the attention mechanism is not used and a separate upsampling mechanism described later is used in its stead. The result is then passed through two uni-directional LSTM layers with ZoneOut. The LSTM output is concatenated with the upsampled encoder output yet again then projected to the mel-spectrogram dimension as frames of a preliminary predicted spectrogram $\\mathbf { { \\mathbf { { \\mathbf { Y } } ^ { \\prime } } } }$ . Once all the mel-spectrogram frames have been predicted, they are passed through a 5-layer batch normalized convolutional post-net with tanh activation on all except the last layer. The post-net predicts a residual to add to the prediction $\\mathbf { { \\mathbf { { \\mathbf { Y } } ^ { \\prime } } } }$ to obtain the final prediction $\\mathbf { Y }$ . ", + "bbox": [ + 173, + 681, + 825, + 888 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In place of the attention mechanism used in Tacotron 2, duration-based models upsample the encoder outputs using per-token duration information. This can be done by simply repeating each encoder output by its duration as in FastSpeech (Ren et al., 2019), but instead we adopt a different process we call Gaussian upsampling, which is described in subsection 3.1. Note that while durations in seconds are used for loss computation, they are converted to durations in integer frames for upsampling. ", + "bbox": [ + 173, + 895, + 823, + 924 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 823, + 146 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For Gaussian upsampling, a duration and a range parameter must be predicted for each token. The range parameter is called thus because it controls the range of a token’s influence. The duration predictor passes the encoder output through two bi-directional LSTM layers followed by a projection layer to predict the numeric duration $\\pmb { d } \\overset { - } { = } ( d _ { 1 } , \\ldots , d _ { N } )$ for each input token. During training, these predicted durations are only used for loss computation, and the target durations are used instead in the upcoming steps2. The range parameter predictor passes the encoder output concatenated with durations through two bi-directional LSTM layers followed by a projection layer and a SoftPlus activation to predict a positive range parameter $\\sigma$ for each input token. ", + "bbox": [ + 174, + 152, + 825, + 265 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After the encoder outputs are upsampled, a Transformer-style sinusoidal positional embedding (Vaswani et al., 2017) is concatenated. The positional embedding tracks the index of each upsampled frame within each token; if the duration values are [2, 1, 3], the indices for the positional embedding would be $[ 1 , 2 , 1 , 1 , 2 , 3 ]$ . ", + "bbox": [ + 174, + 271, + 825, + 328 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The model is trained using a combination of duration prediction loss and mel-spectrogram reconstruction loss. The duration prediction loss is the $L ^ { 2 }$ loss between predicted and target durations in seconds, and the mel-spectrogram reconstruction loss is a $L ^ { 1 } + L ^ { 2 }$ loss between the predicted and the groundtruth mel-spectrogram both before and after the post-net (following Jia et al. (2018)). ", + "bbox": [ + 174, + 333, + 825, + 390 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/77d5689fda722ad82f23fce643109631064942167e12205bbef5e39282facae5.jpg", + "text": "$$\n\\begin{array} { r l r } { { \\mathcal { L } = \\mathcal { L } _ { \\mathrm { s p e c } } + \\lambda _ { \\mathrm { d u r } } \\mathcal { L } _ { \\mathrm { d u r } } } } \\\\ & { } & { \\mathcal { L } _ { \\mathrm { d u r } } = \\frac { 1 } { N } \\| d - d ^ { * } \\| _ { 2 } ^ { 2 } } \\\\ & { } & { \\mathcal { L } _ { \\mathrm { s p e c } } = \\frac { 1 } { T K } \\displaystyle \\sum _ { t = 1 } ^ { T } \\Big ( \\| y _ { t } ^ { \\prime } - y _ { t } ^ { * } \\| _ { 1 } + \\| y _ { t } ^ { \\prime } - y _ { t } ^ { * } \\| _ { 2 } ^ { 2 } + \\| y _ { t } - y _ { t } ^ { * } \\| _ { 1 } + \\| y _ { t } - y _ { t } ^ { * } \\| _ { 2 } ^ { 2 } \\Big ) } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 246, + 396, + 750, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1 GAUSSIAN UPSAMPLING ", + "text_level": 1, + "bbox": [ + 174, + 507, + 385, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a sequence of vectors to be upsampled $\\pmb { H } = ( h _ { 1 } , \\ldots , h _ { N } )$ , integer duration values ${ \\pmb d } =$ $( d _ { 1 } , \\ldots , d _ { N } )$ , and range parameter values ${ \\pmb \\sigma } = ( \\sigma _ { 1 } , \\ldots , \\sigma _ { N } )$ , we compute the upsampled vector sequence $U = ( \\pmb { u } _ { 1 } , \\dots , \\pmb { u } _ { T } )$ as: ", + "bbox": [ + 174, + 534, + 823, + 577 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/63bcb0ec78ed9321ff1048b68ebfe3ff03bd9e476884213da3d4517c1bc7ee3d.jpg", + "text": "$$\nc _ { i } = \\frac { d _ { i } } { 2 } + \\sum _ { j = 1 } ^ { i - 1 } d _ { j } , \\qquad w _ { t i } = \\frac { N \\left( t ; c _ { i } , \\sigma _ { i } ^ { 2 } \\right) } { \\sum _ { j = 1 } ^ { N } \\mathcal { N } \\left( t ; c _ { j } , \\sigma _ { j } ^ { 2 } \\right) } , \\qquad \\quad u _ { t } = \\sum _ { i = 1 } ^ { N } w _ { t i } h _ { i }\n$$", + "text_format": "latex", + "bbox": [ + 235, + 602, + 764, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "That is, we place a Gaussian distribution with standard deviation $\\sigma _ { i }$ at the center of the output segment corresponding to the $i$ -th input token as determined by the duration values $^ d$ , and for each frame we take a weighted sum of the encoder outputs in accordance with the values of Gaussian distributions at that frame. This is similar to the softmax-based aligner in Donahue et al. (2020), except a learned $\\pmb { \\sigma }$ rather than a fixed temperature hyperparameter is used here. ", + "bbox": [ + 173, + 662, + 823, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compared with vanilla upsampling by repetition (as in Ren et al. (2019)), which can be seen as a case of learning a hard monotonic attention, Gaussian upsampling results in an alignment that is more akin to single-component GMM attention. Another benefit of Gaussian upsampling is that it is fully differentiable, which is critical to semi-supervised and unsupervised duration modeling (section 4) as it allows the gradients from the spectrogram losses to flow through to the duration predictor. ", + "bbox": [ + 174, + 739, + 825, + 810 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2 TARGET DURATIONS ", + "text_level": 1, + "bbox": [ + 176, + 829, + 359, + 843 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Neural TTS models using duration need alignments between input tokens and output features. This can be accomplished by implementing an aligner module in the model or by using an external aligner. ", + "bbox": [ + 174, + 856, + 825, + 885 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our work, target durations are extracted by an external, flatstart trained, speaker-dependent HMMbased aligner with a lexicon (Talkin & Wightman, 1994). However, sometimes it is difficult to train a reliable aligner model and/or extract accurate alignments due to data sparsity, poor recording conditions, or unclear pronunciations. To address this problem, we introduce semi-supervised and unsupervised duration modeling. ", + "bbox": [ + 174, + 103, + 825, + 174 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4 SEMI-SUPERVISED AND UNSUPERVISED DURATION MODELING", + "text_level": 1, + "bbox": [ + 176, + 194, + 722, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A na¨ıve approach to unsupervised duration modeling would be to simply train the model using the predicted durations (instead of the target durations) for upsampling, and use only mel-spectrogram reconstruction loss for optimization. To match the length between the predicted durations and the target mel-spectrogram frames, the predicted per-token durations can be scaled by $T / \\sum _ { i } d _ { i }$ . In addition to that, an utterance-level duration loss $\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { u } } = \\frac { 1 } { N } \\left( T - \\sum _ { i } d _ { i } \\right) ^ { 2 } } \\end{array}$ could be added to the total loss. However, experiments show that such an approach does not produce satisfying naturalness in the synthesized speech (subsection 6.3). ", + "bbox": [ + 173, + 224, + 825, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed unsupervised duration modeling is illustrated in Figure 1b. We instead utilize a fine-grained VAE (FVAE) similar to Sun et al. (2020) to model the alignment between the input tokens and the target mel-spectrogram frames, and extract per-token latent features from the target mel-spectrogram based on this alignment. The token encoder output $\\pmb { H }$ is aligned to the target spectrogram $Y ^ { * }$ using an attention mechanism following Lee & Kim (2019): ", + "bbox": [ + 173, + 332, + 825, + 402 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/b10ec1e2c2611610781baea06023ce19aa543c850f920b7d0dee9134c88886a0.jpg", + "text": "$$\n\\begin{array} { r } { \\pmb { c } _ { i } = \\mathrm { A t t n } ( \\pmb { h } _ { i } , f _ { \\mathrm { s p e c } } ( \\pmb { Y } ^ { * } ) ) , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 410, + 407, + 586, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\boldsymbol { h } _ { i }$ is used as the query in the attention, and $f _ { \\mathrm { s p e c } }$ is a spectrogram encoder whose output per frame is used as the values in the attention. A simple dot-product attention from Luong et al. (2015) was used in this work. A latent feature $z _ { i }$ is then computed from $c _ { i }$ and $\\boldsymbol { h } _ { i }$ using a variational auto-encoder (VAE) (Kingma & Welling, 2014) with a Gaussian prior $\\mathcal { N } ( \\mathbf { 0 } , \\mathbf { I } )$ , optimized through the evidence lower bound (ELBO): ", + "bbox": [ + 173, + 430, + 825, + 500 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/5435da12536f1690632bc3ae9f1381dee158dbfd852dd400e54bf24b3cac2b9f.jpg", + "text": "$$\n\\log p \\left( { Y } \\mid { H } \\right) \\geq - \\sum _ { i } D _ { \\mathrm { K L } } \\left( q \\left( \\boldsymbol { z } _ { i } \\mid h _ { i } , \\boldsymbol { c } _ { i } \\right) \\parallel p \\left( \\boldsymbol { z } _ { i } \\right) \\right) + \\mathbb { E } _ { q \\left( \\boldsymbol { z } _ { i } \\mid h _ { i } , \\boldsymbol { c } _ { i } \\right) } \\left[ \\log p \\left( { Y } \\mid { H } , \\boldsymbol { Z } \\right) \\right]\n$$", + "text_format": "latex", + "bbox": [ + 214, + 505, + 784, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the first term is the KL divergence between the prior and posterior, and the second term can be approximated by drawing samples from the posterior. ", + "bbox": [ + 173, + 542, + 825, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Because these latent features are extracted from the target spectrogram with an alignment, they are capable of carrying duration related information. At training time, the per-token duration $^ d$ is predicted from the concatenation of the token encoder output $\\pmb { H }$ and the posterior latent $z$ ; while at inference time, the prior latent is used for $z$ (either sampled from the distribution or using the distribution mode), and the internal attention mechanism of the FVAE is not used. ", + "bbox": [ + 173, + 578, + 825, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unlike Sun et al. (2020), scheduled sampling was not utilized for factorizing latent dimensions. These latent features are only used for duration prediction, and are not used for range parameter prediction or mel-spectrogram reconstruction. We also cap the range parameters for each token to twice its predicted duration in this setup for better training stability. As in section 3, durations predicted in seconds are used for loss computation, but are converted to durations in integer frames for upsampling. ", + "bbox": [ + 174, + 654, + 825, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall loss used for semi-supervised and unsupervised training is thus ", + "bbox": [ + 176, + 744, + 665, + 760 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/140e9778533fa00d85f0cbf04a7f924d478140c02bd0b764d5a8058f4b902d5d.jpg", + "text": "$$\n\\mathcal { L } = \\mathcal { L } _ { \\mathrm { s p e c } } + \\lambda _ { \\mathrm { d u r } } \\mathcal { L } _ { \\mathrm { d u r } } + \\lambda _ { \\mathrm { u } } \\mathcal { L } _ { \\mathrm { u } } + \\lambda _ { \\mathrm { K L } } D _ { \\mathrm { K L } } ,\n$$", + "text_format": "latex", + "bbox": [ + 361, + 766, + 635, + 784 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $D _ { \\mathrm { K L } }$ and $\\mathcal { L } _ { \\mathrm { s p e c } }$ correspond to the first and second terms in Equation 4, respectively, and ${ \\mathcal { L } } _ { \\mathrm { d u r } }$ is only counted for examples with target duration labels (i.e. supervised examples). The last three terms are all weighted per valid token. ", + "bbox": [ + 174, + 787, + 825, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5 ROBUSTNESS EVALUATION ", + "text_level": 1, + "bbox": [ + 176, + 851, + 428, + 866 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Previous work typically evaluated the robustness of TTS systems on a small set of handpicked “hard cases” (He et al., 2019; Zheng et al., 2019; Guo et al., 2019). Although such evaluation is helpful for guiding improvements, it is not reflective of the overall robustness of the system. The handpicked samples may be biased to the weaknesses of a certain system, and is prone to lead further optimization to overfit to the specific evaluation set. ", + "bbox": [ + 174, + 881, + 825, + 924 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 103, + 823, + 132 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this work, we evaluate the robustness of TTS systems on large evaluation sets in an automated way by leveraging existing ASR systems. We run ASR and forced alignment evaluations on the synthesized speech against the verbalized text, and report two metrics measuring over- and under-generation: ", + "bbox": [ + 176, + 138, + 823, + 180 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "1. Unaligned duration ratio (UDR): The synthesized speech is forced aligned with the verbalized input text using an ASR system. Each token in the input text is aligned to a segment in the synthesized audio. Any long audio segments $> 1$ second) not aligned to any input token are typically due to over-generation from the TTS system, such as long pauses, babbling, word repetitions, or failures to stop after finishing the utterance. The total duration of such long unaligned segments divided by the total output duration is the UDR. Note that short unaligned segments are ignored. If the synthesized speech is unable to be aligned with the input text, it is considered as having a UDR of $100 \\%$ . \n2. ASR word deletion rate (WDR): This is the deletion error portion in a standard ASR word error rate (WER) evaluation. Under-generation in the synthesized speech, such as early cutoff and word skipping, is reflected by a higher WDR. ", + "bbox": [ + 212, + 191, + 825, + 351 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As the ASR system will make mistakes, the metrics above are just an upper-bound on the actual failures of the TTS system. ", + "bbox": [ + 174, + 362, + 821, + 390 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6 EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 174, + 411, + 326, + 426 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "All models were trained on a proprietary dataset with 66 speakers with 4 different English accents (US, British, Australian, and Nigerian). The amount of data per speaker varied from merely 5 seconds to 47 hours, totaling 354 hours. ", + "bbox": [ + 174, + 443, + 823, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "A preliminary experiment comparing different attention mechanisms (including monotonic, stepwise monotonic, dynamic convolution and GMM attention (GMMA)) showed that GMMA performed the best. We therefore compared our non-attentive Tacotron not only with Tacotron 2 with locationsensitive attention (LSA) which was used in the original Tacotron 2 paper but also with Tacotron 2 with GMMA. The Tacotron 2 models used reduction factor 2 and $L ^ { 1 } + L ^ { 2 }$ loss. ", + "bbox": [ + 174, + 491, + 825, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following Shen et al. (2018), predicted features were obtained in teacher-forcing mode from a Tacotron 2 model and used to train a WaveRNN vocoder which was then used for all experiments. ", + "bbox": [ + 173, + 568, + 823, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1 NATURALNESS ", + "text_level": 1, + "bbox": [ + 174, + 613, + 318, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The naturalness of the synthesized speech was evaluated through subjective listening tests, including 5-scale Mean Opinion Score (MOS) tests and side-by-side preference tests. The sentences were synthesized using 10 US English speakers (5 male / 5 female) in a round-robin fashion. The amount of training data for the evaluated speakers varied from 3 hours to 47 hours. ", + "bbox": [ + 174, + 640, + 825, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 contains MOS results. Non-Attentive Tacotron with Gaussian upsampling matched Tacotron 2 (GMMA) in naturalness, and both were close to the groundtruth audio. A preference test between ", + "bbox": [ + 169, + 702, + 825, + 731 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4b8e58ac6d446d602ff3d8334b74cf3d278039865d1b7f57219730137751e831.jpg", + "table_caption": [ + "Table 1: MOS with $9 5 \\%$ confidence intervals. " + ], + "table_footnote": [], + "table_body": "
ModelMOS
Tacotron 2
w/LSA4.35 ± 0.05
w/ GMMA4.37 ± 0.04
Non-Attentive Tacotron w/ Gauss. upsampling
w/ vanilla upsampling4.41 ± 0.04
4.13 ± 0.05
Ground truth4.42 ± 0.04
", + "bbox": [ + 189, + 785, + 449, + 915 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/298c40f45176871a5c45d749a449e03d55efe7148d2e82ce9a206d5b085a6fcd.jpg", + "image_caption": [ + "Figure 2: Preference test result with Non-Attentive Tacotron with Gaussian upsampling compared against Tacotron 2 (GMMA). " + ], + "image_footnote": [], + "bbox": [ + 514, + 753, + 795, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Non-Attentive Tacotron and Tacotron 2 (GMMA) further confirmed this result, as shown in Figure 2. Non-Attentive Tacotron with vanilla (repeating) upsampling was rated as significantly less natural than with Gaussian upsampling. ", + "bbox": [ + 176, + 103, + 823, + 147 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The effectiveness of a learned range parameter versus a fixed temperature hyperparameter set at 10.0 as per Donahue et al. (2020) is compared using a preference test in Table 2. While there is only a slight perceived benefit in using a learned range parameter, it reduces the need to tune another dataset-dependent hyperparameter. Additionally, in multi-speaker setups it is possible that the optimal $\\sigma$ may be speaker-dependent. ", + "bbox": [ + 173, + 152, + 825, + 223 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d00bbc13704af7d74258b800af26f713a08cb94947d00f56e960fc3c1f786605.jpg", + "table_caption": [ + "Table 2: Preference test between a learned $\\sigma$ versus a fixed $\\sigma$ set at 10.0. Pace is defined as in subsection 6.2. A negative preference value means that the learned $\\sigma$ is preferred over the fixed $\\sigma$ . " + ], + "table_footnote": [], + "table_body": "
Pace0.8×1.0×1.25×
Preference -0.017 ±0.057 -0.055±0.054 -0.017±0.055
", + "bbox": [ + 277, + 275, + 714, + 316 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2 PACE CONTROL ", + "text_level": 1, + "bbox": [ + 174, + 339, + 321, + 353 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3 shows WER and MOS results after modifying the utterance-wide pace by dividing the predicted durations by various factors. The WER is computed on speech synthesized on transcripts from the LibriTTS test-clean subset with the same 10 speakers in subsection 6.1, and then transcribed by an ASR model described in Park et al. (2020) with a WER of $2 . 3 \\%$ on the ground truth audio. ", + "bbox": [ + 173, + 364, + 472, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "With pace between $0 . 8 \\times - 1 . 2 5 \\times$ , the WERs were hardly impacted. The WER was significantly worse when the pace was increased to $1 . 5 \\times$ normal, partially because the ASR model used was not optimized for speech so fast. In contrast, the subjective MOS decreased rapidly when the pace was sped up or slowed down significantly. However, most of the comments from raters were simply complaining about the pace, such as “too slow to be natural” $\\mathbf { \\eta } ^ { ( 0 . 8 \\mathbf { x } ) }$ or “way too fast” $( 1 . 2 5 \\mathrm { x } )$ . ", + "bbox": [ + 174, + 497, + 472, + 650 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Non-Attentive Tacotron is also able to control the pace of the synthesized speech at a finer granularity, such as per-word or per-phoneme, while still maintain the naturalness of the synthesized speech. Figure 3 shows examples of controlling the pace for specific words in a sentence. ", + "bbox": [ + 173, + 657, + 472, + 753 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/258a479afa848b55bc11081ce643fbccc1c6df42fb7881e28e3ba4917dd524cd.jpg", + "image_caption": [ + "Figure 3: Single word pace control with sentence “I’m so saddened about the devastation in Big Basin.” The top spectrogram is with regular pace. The rest slow down the words “saddened”, “devastation”, and “Big Basin” respectively to $0 . 6 7 \\times$ the regular pace by scaling the predicted duration by $1 . 5 \\times$ . " + ], + "image_footnote": [], + "bbox": [ + 490, + 386, + 818, + 640 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cbfba8b6504066babc85f97147c918ff06051fad774bb865095488b60dcedc0b.jpg", + "table_caption": [ + "Table 3: Performance of controlling the utterance-wide pace of the synthesized speech. " + ], + "table_footnote": [], + "table_body": "
Pace0.67×0.8×0.9×1.0×1.11×1.25×1.5×
WER3.3%2.8%2.6%2.6%2.5%2.7%6.1%
MOS3.28 ± 0.063.87 ± 0.054.24 ± 0.044.41 ± 0.044.28 ± 0.043.79 ± 0.063.18± 0.06
", + "bbox": [ + 174, + 790, + 821, + 844 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.3 SEMI-SUPERVISED AND UNSUPERVISED DURATION MODELING", + "text_level": 1, + "bbox": [ + 176, + 871, + 645, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ten different US English speakers (5 male / 5 female) each with about 4 hours of training data were used for evaluating the performance of the unsupervised and semi-supervised duration modeling. ", + "bbox": [ + 173, + 895, + 821, + 924 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/26daa5ffb38bf9f1cab4ee35f8b59eb8c80db08b72734cb992f60f581080fb60.jpg", + "image_caption": [ + "Figure 4: Alignment on text “What time do I need to show up to my sky diving lesson?” from the unsupervised model. The predicted alignments are from Gaussian upsampling. " + ], + "image_footnote": [], + "bbox": [ + 176, + 99, + 761, + 242 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6176ec827b7d0697c5ef83205c089f8232c9bfbfe329262cbae851cf39b3df79.jpg", + "table_caption": [ + "Table 4: Performance of unsupervised and semi-supervised duration modeling. Zero vectors are used as FVAE latents for inference. MAE denotes the mean absolute error. " + ], + "table_footnote": [], + "table_body": "
TrainingModelDur. MAE (ms)MOS
Unsupervisedw/o FVAE124.42.91± 0.09
w/ FVAE41.34.31 ± 0.04
Semi-supervisedw/o FVAE21.54.19 ± 0.05
Supervisedw/FVAE18.34.35 ± 0.04
Non-Attentive Tacotron15.44.37 ± 0.04
Tacotron2 w/ GMMA-4.35 ± 0.04
Ground truth=4.52 ± 0.03
", + "bbox": [ + 254, + 366, + 740, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The duration labels for these 10 speakers (i.e. about $11 \\%$ of the training data) were withheld for the semi-supervised models, and all duration labels were withheld for the unsupervised models. ", + "bbox": [ + 174, + 546, + 823, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 4 shows predicted alignment after Gaussian upsampling and the internal alignment from the attention module in the FVAE compared with the alignment computed from the target durations, for the unsupervised model. Despite not having access to any target durations, both the FVAE and duration predictor were able to produce an alignment close to that computed from the target durations. ", + "bbox": [ + 174, + 582, + 825, + 637 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Table 4, with the use of the FVAE, the naturalness of both semi-supervised and unsupervised models were very close to that of the supervised models, even though duration prediction errors were higher. The autoregressive decoder trained with teacher forcing may have been powerful enough to correct the duration prediction errors to some degree. However, the naturalness degraded significantly without the use of the FVAE. Although the duration error from the semi-supervised model without FVAE was lower than that from the unsupervised model with FVAE, the former was significantly less natural than the latter. This may be due to a lower consistency between supervised and unsupervised speakers without FVAE. ", + "bbox": [ + 174, + 645, + 825, + 756 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although these models were close to the supervised model in MOS, manual investigation found that samples from both semi-supervised models and unsupervised models had a small chance of containing slight errors that do not occur in the supervised model, such as unclear pronunciations, phoneme repetitions, or extra pauses. However, they are significantly less severe than similar errors from Tacotron 2, mostly impacting just one or a few phonemes. These errors are further confirmed in the large scale robustness evaluation (subsection 6.4). ", + "bbox": [ + 174, + 763, + 825, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The utterance-wide or fine-grained pace control (subsection 6.2) can be applied to the semi-supervised and unsupervised models as well. However, as the alignments are not as accurate, the synthesized speech with fine-grained pace control are not as natural as from the supervised model. The duration may be extended by simply inserting more silence, and the extended portion may include phoneme repetitions or unclear pronunciations. ", + "bbox": [ + 176, + 854, + 823, + 924 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ff0ab9aa5d6d2e0ff69056bfa30b8b097798bd422544d0a80f135e4770ae02b1.jpg", + "table_caption": [ + "Table 5: Robustness measured by UDR and WDR on two large evaluation sets. The evaluation speakers are unsupervised ones in the semi-supervised and unsupervised models. " + ], + "table_footnote": [], + "table_body": "
SystemLibriTTSweb-long
UDR (%)WDR (%)UDR (%)WDR (%)
Tacotron 2
w/LSA16.960.446.044.4
w/ GMMA3.8120.16.1571.3
Non-Attentive Tacotron
Supervised0.0050.10.0111.1
Semi-supervised0.2660.90.6953.5
Unsupervised0.2230.70.5273.2
", + "bbox": [ + 258, + 140, + 735, + 277 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6.4 ROBUSTNESS ", + "text_level": 1, + "bbox": [ + 174, + 314, + 308, + 327 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We evaluated the robustness of the neural TTS models by measuring UDR and WDR on two large evaluation sets: LibriTTS: 354K sentences from all train subsets from the LibriTTS corpus (Zen et al., 2019); and web-long: 100K long sentences mined from the web, which included a small amount of irregular text such as programming code. The median text lengths of the two sets were 74 and 224 characters, respectively. The input was synthesized using the same 10 speakers in subsection 6.3 in a round-robin fashion. All model outputs were capped at 120 seconds. ", + "bbox": [ + 174, + 343, + 825, + 428 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We used the ASR model trained on the LibriSpeech (Panayotov et al., 2015) and LibriLight (Kahn et al., 2020) corpora from Park et al. (2020) for measuring WDR, and a confidence islands-based forced alignment model (Chiu et al., 2018) for measuring UDR. ", + "bbox": [ + 176, + 434, + 825, + 477 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 5 shows the robustness metrics for Tacotron 2 and Non-Attentive Tacotron. Tacotron 2 (LSA) suffered from severe over-generation as measured by UDR, especially on long inputs. Manual investigation uncovered that they were typically long babbling or long silence, often at the end (failure to stop). It also had a high level of under-generation as measured by WDR, typically due to early cutoff. Tacotron 2 (GMMA) performed almost as well as the supervised Non-Attentive Tacotron in WDR because of its soft monotonic nature, which made end-of-sentence prediction easier. However, it still had significantly higher level of over-generation compared to Non-Attentive Tacotron, even when unsupervised or semi-supervised duration modeling is used for the latter. The robustness of semi-supervised and unsupervised Non-Attentive Tacotron is significantly worse than the supervised one. Manual investigation uncovered that the typical failure pattern is that part of the spectrogram is not correctly synthesized (often as silence, but sometimes as babbling), despite that the duration prediction seems reasonable. Such failure pattern contributes to both UDR and WDR. This indicates further improvements to be made. Even then, the semi-supervised and unsupervised Non-Attentive Tacotron still performs significantly better on over-generation compared to Tacotron 2. ", + "bbox": [ + 174, + 483, + 825, + 678 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In practice, we also observed that Tacotron 2 required significantly more care in data preprocessing to achieve this level of robustness, including consistent trimming of leading and trailing silences and filtering out utterances with long pauses. On the other hand, Non-Attentive Tacotron is significantly less sensitive to the data preprocessing steps. ", + "bbox": [ + 176, + 685, + 825, + 741 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7 CONCLUSIONS ", + "text_level": 1, + "bbox": [ + 176, + 773, + 328, + 790 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This paper presented Non-Attentive Tacotron, showing a significant improvement in robustness compared to Tacotron 2 as measured by unaligned duration ratio and word deletion rate, while also slightly outperforming it in naturalness. This was achieved by replacing the attention mechanism in Tacotron 2 with an explicit duration predictor and Gaussian upsampling. We demonstrated the ability to control the pacing of the entire utterance as well as individual words using the duration predictor. We also described a method of modeling duration in a semi-supervised or unsupervised manner using Non-Attentive Tacotron when accurate target duration are scarce or unavailable by using a fine-grained variational auto-encoder, with results almost as good as supervised training. ", + "bbox": [ + 174, + 811, + 825, + 924 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "REFERENCES ", + "text_level": 1, + "bbox": [ + 176, + 103, + 287, + 117 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Sercan O Arik, Mike Chrzanowski, Adam Coates, Gregory Diamos, Andrew Gibiansky, Yongguo Kang, Xian Li, John Miller, Andrew Ng, Jonathan Raiman, Shubho Sengupta, and Mohammad Shoeybi. 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", + "bbox": [ + 176, + 662, + 823, + 705 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "A MODEL PARAMETERS ", + "bbox": [ + 176, + 103, + 393, + 117 + ], + "page_idx": 12 + }, + { + "type": "table", + "img_path": "images/c6130592affe905937e350dff836f4094bc6bf9dad7472a16b4b7d624e43fbdb.jpg", + "table_caption": [ + "Table 6: Model parameters. " + ], + "table_footnote": [], + "table_body": "
CommonTraining modeSynchronous 32
Batch size (per replica) Replicas Parameter init L² regularization Learning rate Learning rate scheduleXavier 1 ×10-6 0.001
Inputs and TargetsOptimizer LSTM zone-out prob LSTM cell abs value cap Sampling rate (Hz) Normalize waveform Pre-emphasis Frame size (ms) Frame hop (ms)decay half every 50K steps. Adam(0.9,0.999,1 × 10-6) 0.1 10.0 24,000 No No 50
EncoderMel channels K Mel frequency lower bound (Hz) Mel frequency upper bound (Hz)128 20 12,000
FVAE
Yes
512×2
5×1
512 64
Mel spectrogram dynamic range compressionlog(x +0.001)
Token embedding dim
Speaker embedding dim
Conv kernel
Conv dim[512, 512, 512]
Conv activation[None,None,None]
Conv batch norm decay0.999
Bi-LSTM dim
Segment encoder conv kernel3×1
Segment encoder conv dim[512,512,512]
Segment encoder Bi-LSTM dim256×2
Layer norm attention inputs
Latent dim8 projected to 16
Duration PredictorBi-LSTM dim512×2
Projection activationNone
Xdur supervised2.0
Xdur semi-supervised100.0
100.0
Au semi-supervised1×10-3
XKL semi-supervised
Xu unsupervised1.0
Range Parameter Predictor入KL unsupervised1 ×10-4
Bi-LSTM dim512×2
Positional EmbeddingProjection activationSoftPlus
Embedding dim32
Timestep denominator10.000
Decoder[256,256]
Pre-net dim supervised
Pre-net dim semi/unsupervised[128,128]
Pre-net activation[ReLU,ReLU]
[0.5,0.5]
Pre-net dropout prob
LSTM dim^1,024
LSTM inituniform(0.1)
Projection inituniform(0.1)
Post-net conv kernel5×1
Post-net conv dim
[512,512,512,512,128]
Post-net conv activation
[tanh,tanh,tanh,tanh,None]
Post-net conv init
", + "bbox": [ + 176, + 154, + 825, + 900 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "B WER BREAKDOWNS IN THE ROBUSTNESS EVALUATION ", + "text_level": 1, + "bbox": [ + 173, + 103, + 666, + 118 + ], + "page_idx": 13 + }, + { + "type": "table", + "img_path": "images/17cbaf3bc0c0241f4b4c555eff7c23510fbae1b714bc74220e5117554de38d48.jpg", + "table_caption": [ + "Table 7: WER breakdowns in the robustness evaluation. Deletion rate (del) is the WDR in Table 5. " + ], + "table_footnote": [], + "table_body": "
SystemLibriTTSweb-long
WERdelinssubWERdelinssub
Tacotron 2
w/LSA1.80.40.31.113.04.42.06.7
w/ GMMA1.70.10.11.510.11.31.37.4
Non-Attentive Tacotron
Supervised1.40.10.11.29.31.11.36.9
Semi-supervised3.30.90.22.214.13.51.69.0
Unsupervised3.50.70.32.615.33.22.010.1
", + "bbox": [ + 243, + 164, + 750, + 301 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "C CLASSIFICATION OF SOME TTS MODELS ", + "text_level": 1, + "bbox": [ + 173, + 327, + 547, + 344 + ], + "page_idx": 13 + }, + { + "type": "table", + "img_path": "images/650fa3d110c757c51bd5816919576387ca5e97e7e47e9826639887382164ddce.jpg", + "table_caption": [ + "Table 8: Classification of some TTS models into autoregressive (AR)/feed-forward (FF), RNN/Transformer/fully convolutional, and attention-based/duration-based. " + ], + "table_footnote": [], + "table_body": "
ModelYearARFFRNNTransformerFull ConvAttentionDuration
Deep Voice2017
Char2Wav2017
Tacotron2017
Deep Voice 22017
Tacotron 22018
Deep Voice 32018
Transformer TTS2019
CHiVE2019
DurIAN2019
Fastspeech2019
TalkNet2020
AlignTTS2020
JDI-T2020
Non-Attentive Tacotron2020
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A side benefit of such a duration predictor is that it is significantly more resilient to the", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 692, + 279, + 705 + ], + "spans": [ + { + "bbox": [ + 106, + 692, + 279, + 705 + ], + "score": 1.0, + "content": "failures afflicting the attention mechanism.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 649, + 506, + 705 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 709, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "score": 1.0, + "content": "However, one-to-many regression problems like TTS can benefit from an autoregressive decoder as", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "the previous mel-spectrogram frames provides context to disambiguate between multi-modal outputs.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5, + "bbox_fs": [ + 106, + 710, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 504, + 105 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "In this paper, we propose, Non-Attentive Tacotron1, a neural TTS model that combines the robust", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 442, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 442, + 106 + ], + "score": 1.0, + "content": "duration predictor with the autoregressive decoder of Tacotron 2 (Shen et al., 2018).", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 108, + 110, + 504, + 143 + ], + "lines": [ + { + "bbox": [ + 105, + 109, + 505, + 124 + ], + "spans": [ + { + "bbox": [ + 105, + 109, + 505, + 124 + ], + "score": 1.0, + "content": "Our work is similar to DurIAN (Yu et al., 2019; Zhang et al., 2020), which incorporates the duration", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 121, + 505, + 134 + ], + "spans": [ + { + "bbox": [ + 106, + 121, + 505, + 134 + ], + "score": 1.0, + "content": "predictor with an autoregressive decoder. 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Introduction of Gaussian upsampling significantly improving the naturalness compared to", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 142, + 214, + 298, + 226 + ], + "spans": [ + { + "bbox": [ + 142, + 214, + 298, + 226 + ], + "score": 1.0, + "content": "vanilla upsampling through repetition;", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 129, + 232, + 408, + 246 + ], + "spans": [ + { + "bbox": [ + 129, + 232, + 408, + 246 + ], + "score": 1.0, + "content": "3. Global and fine-grained controlling of durations at inference time;", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 128, + 250, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 128, + 250, + 505, + 264 + ], + "score": 1.0, + "content": "4. Semi-supervised and unsupervised duration modeling of Non-Attentive Tacotron, allowing", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 262, + 401, + 275 + ], + "spans": [ + { + "bbox": [ + 141, + 262, + 401, + 275 + ], + "score": 1.0, + "content": "the model to be trained with few to no duration annotations; and", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 129, + 281, + 506, + 294 + ], + "spans": [ + { + "bbox": [ + 129, + 281, + 506, + 294 + ], + "score": 1.0, + "content": "5. More reliable evaluation metrics for measuring robustness of TTS models, as well as", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 292, + 470, + 305 + ], + "spans": [ + { + "bbox": [ + 141, + 292, + 470, + 305 + ], + "score": 1.0, + "content": "comparing Non-Attentive Tacotron with Tacotron 2 with respect to those metrics.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 10 + }, + { + "type": "title", + "bbox": [ + 108, + 324, + 217, + 336 + ], + "lines": [ + { + "bbox": [ + 104, + 322, + 219, + 339 + ], + "spans": [ + { + "bbox": [ + 104, + 322, + 219, + 339 + ], + "score": 1.0, + "content": "2 RELATED WORKS", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 351, + 505, + 429 + ], + "lines": [ + { + "bbox": [ + 106, + 352, + 505, + 364 + ], + "spans": [ + { + "bbox": [ + 106, + 352, + 505, + 364 + ], + "score": 1.0, + "content": "In the past decade, model-based TTS synthesis has evolved from hidden Markov model (HMM)-based", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 362, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 506, + 376 + ], + "score": 1.0, + "content": "approaches (Zen et al., 2009) to using deep neural networks. Over this period, the concept of using", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 374, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 505, + 387 + ], + "score": 1.0, + "content": "an explicit representation of token (phoneme) durations has not been foreign. Early neural parametric", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 385, + 505, + 397 + ], + "spans": [ + { + "bbox": [ + 106, + 385, + 505, + 397 + ], + "score": 1.0, + "content": "synthesis models (Zen et al., 2013) require explicit alignments between input and target and include", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 396, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 106, + 396, + 505, + 408 + ], + "score": 1.0, + "content": "durations as part of the bag of features used to generate vocoder parameters. Explicit durations", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 407, + 506, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 419 + ], + "score": 1.0, + "content": "continue to be used with the advent of the end-to-end neural vocoder WaveNet (Oord et al., 2016) in", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 418, + 506, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 418, + 506, + 430 + ], + "score": 1.0, + "content": "works such as Deep Voice (Arik et al., 2017; Gibiansky et al., 2017) and CHiVE (Kenter et al., 2019).", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 434, + 505, + 523 + ], + "lines": [ + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "score": 1.0, + "content": "As general focus turned towards end-to-end approaches, the autoregressive sequence-to-sequence", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 445, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 445, + 505, + 457 + ], + "score": 1.0, + "content": "model with attention mechanism used in neural machine translation (NMT) (Bahdanau et al., 2015)", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 455, + 506, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 470 + ], + "score": 1.0, + "content": "and automatic speech recognition (ASR) (Chan et al., 2016) became an attractive option, removing", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 468, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 506, + 480 + ], + "score": 1.0, + "content": "the need to represent durations explicitly. This led to works such as Char2Wav (Sotelo et al., 2017),", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 478, + 506, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 506, + 491 + ], + "score": 1.0, + "content": "Tacotron (Wang et al., 2017; Shen et al., 2018), Deep Voice 3 (Ping et al., 2018), and Transformer", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 489, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 506, + 502 + ], + "score": 1.0, + "content": "TTS (Li et al., 2019). 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Introduction of Gaussian upsampling significantly improving the naturalness compared to", + "type": "text" + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 142, + 214, + 298, + 226 + ], + "spans": [ + { + "bbox": [ + 142, + 214, + 298, + 226 + ], + "score": 1.0, + "content": "vanilla upsampling through repetition;", + "type": "text" + } + ], + "index": 9, + "is_list_end_line": true + }, + { + "bbox": [ + 129, + 232, + 408, + 246 + ], + "spans": [ + { + "bbox": [ + 129, + 232, + 408, + 246 + ], + "score": 1.0, + "content": "3. Global and fine-grained controlling of durations at inference time;", + "type": "text" + } + ], + "index": 10, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 128, + 250, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 128, + 250, + 505, + 264 + ], + "score": 1.0, + "content": "4. Semi-supervised and unsupervised duration modeling of Non-Attentive Tacotron, allowing", + "type": "text" + } + ], + "index": 11, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 262, + 401, + 275 + ], + "spans": [ + { + "bbox": [ + 141, + 262, + 401, + 275 + ], + "score": 1.0, + "content": "the model to be trained with few to no duration annotations; and", + "type": "text" + } + ], + "index": 12, + "is_list_end_line": true + }, + { + "bbox": [ + 129, + 281, + 506, + 294 + ], + "spans": [ + { + "bbox": [ + 129, + 281, + 506, + 294 + ], + "score": 1.0, + "content": "5. More reliable evaluation metrics for measuring robustness of TTS models, as well as", + "type": "text" + } + ], + "index": 13, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 292, + 470, + 305 + ], + "spans": [ + { + "bbox": [ + 141, + 292, + 470, + 305 + ], + "score": 1.0, + "content": "comparing Non-Attentive Tacotron with Tacotron 2 with respect to those metrics.", + "type": "text" + } + ], + "index": 14, + "is_list_end_line": true + } + ], + "index": 10, + "bbox_fs": [ + 128, + 172, + 506, + 305 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 324, + 217, + 336 + ], + "lines": [ + { + "bbox": [ + 104, + 322, + 219, + 339 + ], + "spans": [ + { + "bbox": [ + 104, + 322, + 219, + 339 + ], + "score": 1.0, + "content": "2 RELATED WORKS", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 351, + 505, + 429 + ], + "lines": [ + { + "bbox": [ + 106, + 352, + 505, + 364 + ], + "spans": [ + { + "bbox": [ + 106, + 352, + 505, + 364 + ], + "score": 1.0, + "content": "In the past decade, model-based TTS synthesis has evolved from hidden Markov model (HMM)-based", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 362, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 506, + 376 + ], + "score": 1.0, + "content": "approaches (Zen et al., 2009) to using deep neural networks. Over this period, the concept of using", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 374, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 505, + 387 + ], + "score": 1.0, + "content": "an explicit representation of token (phoneme) durations has not been foreign. Early neural parametric", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 385, + 505, + 397 + ], + "spans": [ + { + "bbox": [ + 106, + 385, + 505, + 397 + ], + "score": 1.0, + "content": "synthesis models (Zen et al., 2013) require explicit alignments between input and target and include", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 396, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 106, + 396, + 505, + 408 + ], + "score": 1.0, + "content": "durations as part of the bag of features used to generate vocoder parameters. Explicit durations", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 407, + 506, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 419 + ], + "score": 1.0, + "content": "continue to be used with the advent of the end-to-end neural vocoder WaveNet (Oord et al., 2016) in", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 418, + 506, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 418, + 506, + 430 + ], + "score": 1.0, + "content": "works such as Deep Voice (Arik et al., 2017; Gibiansky et al., 2017) and CHiVE (Kenter et al., 2019).", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 19, + "bbox_fs": [ + 105, + 352, + 506, + 430 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 434, + 505, + 523 + ], + "lines": [ + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "score": 1.0, + "content": "As general focus turned towards end-to-end approaches, the autoregressive sequence-to-sequence", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 445, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 445, + 505, + 457 + ], + "score": 1.0, + "content": "model with attention mechanism used in neural machine translation (NMT) (Bahdanau et al., 2015)", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 455, + 506, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 470 + ], + "score": 1.0, + "content": "and automatic speech recognition (ASR) (Chan et al., 2016) became an attractive option, removing", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 468, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 506, + 480 + ], + "score": 1.0, + "content": "the need to represent durations explicitly. This led to works such as Char2Wav (Sotelo et al., 2017),", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 478, + 506, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 506, + 491 + ], + "score": 1.0, + "content": "Tacotron (Wang et al., 2017; Shen et al., 2018), Deep Voice 3 (Ping et al., 2018), and Transformer", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 489, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 506, + 502 + ], + "score": 1.0, + "content": "TTS (Li et al., 2019). Similar models have been used for more complicated problems, like direct", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 500, + 506, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 506, + 513 + ], + "score": 1.0, + "content": "speech-to-speech translation (Jia et al., 2019), speech conversion (Biadsy et al., 2019), and speech", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 512, + 240, + 524 + ], + "spans": [ + { + "bbox": [ + 106, + 512, + 240, + 524 + ], + "score": 1.0, + "content": "enhancement (Ding et al., 2020).", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 26.5, + "bbox_fs": [ + 105, + 434, + 506, + 524 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 528, + 503, + 561 + ], + "lines": [ + { + "bbox": [ + 106, + 529, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 529, + 505, + 540 + ], + "score": 1.0, + "content": "Tacotron 2, on which our work is based, is one such model. 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See Appendix C for a rough categorization of", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 610, + 163, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 163, + 621 + ], + "score": 1.0, + "content": "these models.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 36, + "bbox_fs": [ + 105, + 567, + 506, + 621 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 628, + 505, + 705 + ], + "lines": [ + { + "bbox": [ + 106, + 628, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 506, + 640 + ], + "score": 1.0, + "content": "To train the duration predictor, FastSpeech uses target durations extracted from a pre-trained autore-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 639, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 639, + 505, + 651 + ], + "score": 1.0, + "content": "gressive model in teacher forcing mode, while JDI-T also extracts target durations from a separate", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 650, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 650, + 505, + 662 + ], + "score": 1.0, + "content": "autoregressive model but co-trains it with the feed-forward model. 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This paper focuses on the feature generation network, and can be used with", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 407, + 506, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 419 + ], + "score": 1.0, + "content": "any vocoder network, e.g., WaveNet (Oord et al., 2016), WaveRNN (Kalchbrenner et al., 2018),", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 417, + 506, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 417, + 506, + 430 + ], + "score": 1.0, + "content": "WaveGlow (Prenger et al., 2019), MelGAN (Kumar et al., 2019), or WaveGrad (Chen et al., 2020).", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 428, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 505, + 442 + ], + "score": 1.0, + "content": "The architecture of Non-Attentive Tacotron is illustrated in Figure 1a. 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The", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 489, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 505, + 502 + ], + "score": 1.0, + "content": "ids are used to index into a learned embedding and is then passed through an encoder consisting of 3", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 500, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 116, + 511 + ], + "score": 0.72, + "content": "\\times", + "type": "inline_equation" + }, + { + "bbox": [ + 117, + 500, + 505, + 513 + ], + "score": 1.0, + "content": "(dropout, batch normalization, convolution) layers followed by a single bi-directional LSTM with", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 511, + 506, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 321, + 524 + ], + "score": 1.0, + "content": "ZoneOut to generate a 2-dimensional output of length", + "type": "text" + }, + { + "bbox": [ + 321, + 512, + 331, + 521 + ], + "score": 0.8, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 331, + 511, + 506, + 524 + ], + "score": 1.0, + "content": ". 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The last three terms", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 647, + 236, + 659 + ], + "spans": [ + { + "bbox": [ + 106, + 647, + 236, + 659 + ], + "score": 1.0, + "content": "are all weighted per valid token.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 43, + "bbox_fs": [ + 105, + 624, + 506, + 659 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 674, + 262, + 686 + ], + "lines": [ + { + "bbox": [ + 105, + 673, + 264, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 673, + 264, + 689 + ], + "score": 1.0, + "content": "5 ROBUSTNESS EVALUATION", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 45 + }, + { + "type": "text", + "bbox": [ + 107, + 698, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "Previous work typically evaluated the robustness of TTS systems on a small set of handpicked “hard", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "cases” (He et al., 2019; Zheng et al., 2019; Guo et al., 2019). Although such evaluation is helpful for", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "guiding improvements, it is not reflective of the overall robustness of the system. The handpicked", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "samples may be biased to the weaknesses of a certain system, and is prone to lead further optimization", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 95, + 262, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 95, + 262, + 106 + ], + "score": 1.0, + "content": "to overfit to the specific evaluation set.", + "type": "text", + "cross_page": true + } + ], + "index": 1 + } + ], + "index": 47, + "bbox_fs": [ + 105, + 698, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 504, + 105 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "samples may be biased to the weaknesses of a certain system, and is prone to lead further optimization", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 95, + 262, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 95, + 262, + 106 + ], + "score": 1.0, + "content": "to overfit to the specific evaluation set.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 108, + 110, + 504, + 143 + ], + "lines": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "score": 1.0, + "content": "In this work, we evaluate the robustness of TTS systems on large evaluation sets in an automated way", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 122, + 505, + 134 + ], + "spans": [ + { + "bbox": [ + 106, + 122, + 505, + 134 + ], + "score": 1.0, + "content": "by leveraging existing ASR systems. 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Each token in the input text is aligned to a", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 141, + 176, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 141, + 176, + 381, + 189 + ], + "score": 1.0, + "content": "segment in the synthesized audio. Any long audio segments", + "type": "text" + }, + { + "bbox": [ + 382, + 176, + 399, + 186 + ], + "score": 0.85, + "content": "> 1", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "second) not aligned to any", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 186, + 506, + 199 + ], + "spans": [ + { + "bbox": [ + 141, + 186, + 506, + 199 + ], + "score": 1.0, + "content": "input token are typically due to over-generation from the TTS system, such as long pauses,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 141, + 197, + 506, + 210 + ], + "spans": [ + { + "bbox": [ + 141, + 197, + 506, + 210 + ], + "score": 1.0, + "content": "babbling, word repetitions, or failures to stop after finishing the utterance. The total duration", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 208, + 506, + 221 + ], + "spans": [ + { + "bbox": [ + 141, + 208, + 506, + 221 + ], + "score": 1.0, + "content": "of such long unaligned segments divided by the total output duration is the UDR. Note that", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 141, + 219, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 141, + 219, + 505, + 232 + ], + "score": 1.0, + "content": "short unaligned segments are ignored. 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Under-generation in the synthesized speech, such as early", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 267, + 370, + 279 + ], + "spans": [ + { + "bbox": [ + 141, + 267, + 370, + 279 + ], + "score": 1.0, + "content": "cutoff and word skipping, is reflected by a higher WDR.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 287, + 503, + 309 + ], + "lines": [ + { + "bbox": [ + 106, + 287, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 287, + 505, + 300 + ], + "score": 1.0, + "content": "As the ASR system will make mistakes, the metrics above are just an upper-bound on the actual", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 297, + 217, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 297, + 217, + 311 + ], + "score": 1.0, + "content": "failures of the TTS system.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16.5 + }, + { + "type": "title", + "bbox": [ + 107, + 326, + 200, + 338 + ], + "lines": [ + { + "bbox": [ + 105, + 326, + 201, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 201, + 340 + ], + "score": 1.0, + "content": "6 EXPERIMENTS", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 351, + 504, + 384 + ], + "lines": [ + { + "bbox": [ + 106, + 351, + 504, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 351, + 504, + 363 + ], + "score": 1.0, + "content": "All models were trained on a proprietary dataset with 66 speakers with 4 different English accents", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 361, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 505, + 375 + ], + "score": 1.0, + "content": "(US, British, Australian, and Nigerian). The amount of data per speaker varied from merely 5 seconds", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 372, + 234, + 385 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 234, + 385 + ], + "score": 1.0, + "content": "to 47 hours, totaling 354 hours.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 389, + 505, + 445 + ], + "lines": [ + { + "bbox": [ + 106, + 390, + 505, + 402 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 505, + 402 + ], + "score": 1.0, + "content": "A preliminary experiment comparing different attention mechanisms (including monotonic, stepwise", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 400, + 505, + 413 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 505, + 413 + ], + "score": 1.0, + "content": "monotonic, dynamic convolution and GMM attention (GMMA)) showed that GMMA performed", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 410, + 506, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 506, + 424 + ], + "score": 1.0, + "content": "the best. 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ModelMOS
Tacotron 2
w/LSA4.35 ± 0.05
w/ GMMA4.37 ± 0.04
Non-Attentive Tacotron w/ Gauss. upsampling
w/ vanilla upsampling4.41 ± 0.04
4.13 ± 0.05
Ground truth4.42 ± 0.04
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Any long audio segments", + "type": "text" + }, + { + "bbox": [ + 382, + 176, + 399, + 186 + ], + "score": 0.85, + "content": "> 1", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "second) not aligned to any", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 186, + 506, + 199 + ], + "spans": [ + { + "bbox": [ + 141, + 186, + 506, + 199 + ], + "score": 1.0, + "content": "input token are typically due to over-generation from the TTS system, such as long pauses,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 141, + 197, + 506, + 210 + ], + "spans": [ + { + "bbox": [ + 141, + 197, + 506, + 210 + ], + "score": 1.0, + "content": "babbling, word repetitions, or failures to stop after finishing the utterance. The total duration", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 208, + 506, + 221 + ], + "spans": [ + { + "bbox": [ + 141, + 208, + 506, + 221 + ], + "score": 1.0, + "content": "of such long unaligned segments divided by the total output duration is the UDR. Note that", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 141, + 219, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 141, + 219, + 505, + 232 + ], + "score": 1.0, + "content": "short unaligned segments are ignored. If the synthesized speech is unable to be aligned with", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 142, + 230, + 372, + 242 + ], + "spans": [ + { + "bbox": [ + 142, + 230, + 344, + 242 + ], + "score": 1.0, + "content": "the input text, it is considered as having a UDR of", + "type": "text" + }, + { + "bbox": [ + 344, + 230, + 368, + 240 + ], + "score": 0.88, + "content": "100 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 230, + 372, + 242 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 12, + "is_list_end_line": true + }, + { + "bbox": [ + 130, + 244, + 505, + 257 + ], + "spans": [ + { + "bbox": [ + 130, + 244, + 505, + 257 + ], + "score": 1.0, + "content": "2. ASR word deletion rate (WDR): This is the deletion error portion in a standard ASR word", + "type": "text" + } + ], + "index": 13, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 256, + 505, + 268 + ], + "spans": [ + { + "bbox": [ + 141, + 256, + 505, + 268 + ], + "score": 1.0, + "content": "error rate (WER) evaluation. Under-generation in the synthesized speech, such as early", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 267, + 370, + 279 + ], + "spans": [ + { + "bbox": [ + 141, + 267, + 370, + 279 + ], + "score": 1.0, + "content": "cutoff and word skipping, is reflected by a higher WDR.", + "type": "text" + } + ], + "index": 15, + "is_list_end_line": true + } + ], + "index": 10, + "bbox_fs": [ + 130, + 154, + 506, + 279 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 287, + 503, + 309 + ], + "lines": [ + { + "bbox": [ + 106, + 287, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 287, + 505, + 300 + ], + "score": 1.0, + "content": "As the ASR system will make mistakes, the metrics above are just an upper-bound on the actual", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 297, + 217, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 297, + 217, + 311 + ], + "score": 1.0, + "content": "failures of the TTS system.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16.5, + "bbox_fs": [ + 105, + 287, + 505, + 311 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 326, + 200, + 338 + ], + "lines": [ + { + "bbox": [ + 105, + 326, + 201, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 201, + 340 + ], + "score": 1.0, + "content": "6 EXPERIMENTS", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 351, + 504, + 384 + ], + "lines": [ + { + "bbox": [ + 106, + 351, + 504, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 351, + 504, + 363 + ], + "score": 1.0, + "content": "All models were trained on a proprietary dataset with 66 speakers with 4 different English accents", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 361, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 505, + 375 + ], + "score": 1.0, + "content": "(US, British, Australian, and Nigerian). The amount of data per speaker varied from merely 5 seconds", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 372, + 234, + 385 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 234, + 385 + ], + "score": 1.0, + "content": "to 47 hours, totaling 354 hours.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20, + "bbox_fs": [ + 105, + 351, + 505, + 385 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 389, + 505, + 445 + ], + "lines": [ + { + "bbox": [ + 106, + 390, + 505, + 402 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 505, + 402 + ], + "score": 1.0, + "content": "A preliminary experiment comparing different attention mechanisms (including monotonic, stepwise", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 400, + 505, + 413 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 505, + 413 + ], + "score": 1.0, + "content": "monotonic, dynamic convolution and GMM attention (GMMA)) showed that GMMA performed", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 410, + 506, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 506, + 424 + ], + "score": 1.0, + "content": "the best. We therefore compared our non-attentive Tacotron not only with Tacotron 2 with location-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 423, + 506, + 434 + ], + "spans": [ + { + "bbox": [ + 106, + 423, + 506, + 434 + ], + "score": 1.0, + "content": "sensitive attention (LSA) which was used in the original Tacotron 2 paper but also with Tacotron 2", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 433, + 426, + 445 + ], + "spans": [ + { + "bbox": [ + 106, + 433, + 369, + 445 + ], + "score": 1.0, + "content": "with GMMA. The Tacotron 2 models used reduction factor 2 and", + "type": "text" + }, + { + "bbox": [ + 369, + 433, + 405, + 444 + ], + "score": 0.92, + "content": "L ^ { 1 } + L ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 433, + 426, + 445 + ], + "score": 1.0, + "content": "loss.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 390, + 506, + 445 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 450, + 504, + 472 + ], + "lines": [ + { + "bbox": [ + 106, + 450, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 505, + 462 + ], + "score": 1.0, + "content": "Following Shen et al. (2018), predicted features were obtained in teacher-forcing mode from a", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 460, + 499, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 499, + 474 + ], + "score": 1.0, + "content": "Tacotron 2 model and used to train a WaveRNN vocoder which was then used for all experiments.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 450, + 505, + 474 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 486, + 195, + 497 + ], + "lines": [ + { + "bbox": [ + 105, + 485, + 196, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 485, + 196, + 499 + ], + "score": 1.0, + "content": "6.1 NATURALNESS", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 107, + 507, + 505, + 551 + ], + "lines": [ + { + "bbox": [ + 105, + 506, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 505, + 520 + ], + "score": 1.0, + "content": "The naturalness of the synthesized speech was evaluated through subjective listening tests, including", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 517, + 506, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 506, + 531 + ], + "score": 1.0, + "content": "5-scale Mean Opinion Score (MOS) tests and side-by-side preference tests. The sentences were", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 529, + 506, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 506, + 541 + ], + "score": 1.0, + "content": "synthesized using 10 US English speakers (5 male / 5 female) in a round-robin fashion. The amount", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 540, + 406, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 406, + 552 + ], + "score": 1.0, + "content": "of training data for the evaluated speakers varied from 3 hours to 47 hours.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31.5, + "bbox_fs": [ + 105, + 506, + 506, + 552 + ] + }, + { + "type": "text", + "bbox": [ + 104, + 556, + 505, + 579 + ], + "lines": [ + { + "bbox": [ + 106, + 557, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 106, + 557, + 505, + 568 + ], + "score": 1.0, + "content": "Table 1 contains MOS results. Non-Attentive Tacotron with Gaussian upsampling matched Tacotron 2", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 567, + 505, + 580 + ], + "spans": [ + { + "bbox": [ + 105, + 567, + 505, + 580 + ], + "score": 1.0, + "content": "(GMMA) in naturalness, and both were close to the groundtruth audio. A preference test between", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34.5, + "bbox_fs": [ + 105, + 557, + 505, + 580 + ] + }, + { + "type": "table", + "bbox": [ + 116, + 622, + 275, + 725 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 601, + 285, + 613 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 601, + 287, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 601, + 183, + 614 + ], + "score": 1.0, + "content": "Table 1: MOS with", + "type": "text" + }, + { + "bbox": [ + 184, + 602, + 203, + 612 + ], + "score": 0.85, + "content": "9 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 601, + 287, + 614 + ], + "score": 1.0, + "content": "confidence intervals.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "table_body", + "bbox": [ + 116, + 622, + 275, + 725 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 116, + 622, + 275, + 725 + ], + "spans": [ + { + "bbox": [ + 116, + 622, + 275, + 725 + ], + "score": 0.975, + "html": "
ModelMOS
Tacotron 2
w/LSA4.35 ± 0.05
w/ GMMA4.37 ± 0.04
Non-Attentive Tacotron w/ Gauss. upsampling
w/ vanilla upsampling4.41 ± 0.04
4.13 ± 0.05
Ground truth4.42 ± 0.04
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Additionally, in multi-speaker setups it is possible that the optimal", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 165, + 225, + 178 + ], + "spans": [ + { + "bbox": [ + 106, + 167, + 114, + 175 + ], + "score": 0.66, + "content": "\\sigma", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 165, + 225, + 178 + ], + "score": 1.0, + "content": "may be speaker-dependent.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 170, + 218, + 437, + 251 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 186, + 504, + 209 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 186, + 505, + 198 + ], + "spans": [ + { + "bbox": [ + 106, + 186, + 286, + 198 + ], + "score": 1.0, + "content": "Table 2: Preference test between a learned", + "type": "text" + }, + { + "bbox": [ + 287, + 189, + 294, + 196 + ], + "score": 0.7, + "content": "\\sigma", + "type": "inline_equation" + }, + { + "bbox": [ + 295, + 186, + 356, + 198 + ], + "score": 1.0, + "content": "versus a fixed", + "type": "text" + }, + { + "bbox": [ + 357, + 189, + 365, + 196 + ], + "score": 0.71, + "content": "\\sigma", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 186, + 505, + 198 + ], + "score": 1.0, + "content": "set at 10.0. Pace is defined as in", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 197, + 500, + 210 + ], + "spans": [ + { + "bbox": [ + 106, + 197, + 374, + 210 + ], + "score": 1.0, + "content": "subsection 6.2. 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Pace0.8×1.0×1.25×
Preference -0.017 ±0.057 -0.055±0.054 -0.017±0.055
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Pace0.67×0.8×0.9×1.0×1.11×1.25×1.5×
WER3.3%2.8%2.6%2.6%2.5%2.7%6.1%
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Pace0.8×1.0×1.25×
Preference -0.017 ±0.057 -0.055±0.054 -0.017±0.055
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Pace0.67×0.8×0.9×1.0×1.11×1.25×1.5×
WER3.3%2.8%2.6%2.6%2.5%2.7%6.1%
MOS3.28 ± 0.063.87 ± 0.054.24 ± 0.044.41 ± 0.044.28 ± 0.043.79 ± 0.063.18± 0.06
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TrainingModelDur. MAE (ms)MOS
Unsupervisedw/o FVAE124.42.91± 0.09
w/ FVAE41.34.31 ± 0.04
Semi-supervisedw/o FVAE21.54.19 ± 0.05
Supervisedw/FVAE18.34.35 ± 0.04
Non-Attentive Tacotron15.44.37 ± 0.04
Tacotron2 w/ GMMA-4.35 ± 0.04
Ground truth=4.52 ± 0.03
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TrainingModelDur. MAE (ms)MOS
Unsupervisedw/o FVAE124.42.91± 0.09
w/ FVAE41.34.31 ± 0.04
Semi-supervisedw/o FVAE21.54.19 ± 0.05
Supervisedw/FVAE18.34.35 ± 0.04
Non-Attentive Tacotron15.44.37 ± 0.04
Tacotron2 w/ GMMA-4.35 ± 0.04
Ground truth=4.52 ± 0.03
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SystemLibriTTSweb-long
UDR (%)WDR (%)UDR (%)WDR (%)
Tacotron 2
w/LSA16.960.446.044.4
w/ GMMA3.8120.16.1571.3
Non-Attentive Tacotron
Supervised0.0050.10.0111.1
Semi-supervised0.2660.90.6953.5
Unsupervised0.2230.70.5273.2
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The median text lengths of the two sets were 74 and 224", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 317, + 506, + 330 + ], + "spans": [ + { + "bbox": [ + 106, + 317, + 506, + 330 + ], + "score": 1.0, + "content": "characters, respectively. The input was synthesized using the same 10 speakers in subsection 6.3 in a", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 328, + 381, + 339 + ], + "spans": [ + { + "bbox": [ + 106, + 328, + 381, + 339 + ], + "score": 1.0, + "content": "round-robin fashion. All model outputs were capped at 120 seconds.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 108, + 344, + 505, + 378 + ], + "lines": [ + { + "bbox": [ + 106, + 344, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 505, + 357 + ], + "score": 1.0, + "content": "We used the ASR model trained on the LibriSpeech (Panayotov et al., 2015) and LibriLight (Kahn", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 355, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 505, + 369 + ], + "score": 1.0, + "content": "et al., 2020) corpora from Park et al. (2020) for measuring WDR, and a confidence islands-based", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 367, + 363, + 379 + ], + "spans": [ + { + "bbox": [ + 106, + 367, + 363, + 379 + ], + "score": 1.0, + "content": "forced alignment model (Chiu et al., 2018) for measuring UDR.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 107, + 383, + 505, + 537 + ], + "lines": [ + { + "bbox": [ + 106, + 383, + 505, + 395 + ], + "spans": [ + { + "bbox": [ + 106, + 383, + 505, + 395 + ], + "score": 1.0, + "content": "Table 5 shows the robustness metrics for Tacotron 2 and Non-Attentive Tacotron. Tacotron 2 (LSA)", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 395, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 106, + 395, + 506, + 408 + ], + "score": 1.0, + "content": "suffered from severe over-generation as measured by UDR, especially on long inputs. Manual", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 405, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 505, + 419 + ], + "score": 1.0, + "content": "investigation uncovered that they were typically long babbling or long silence, often at the end (failure", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 417, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 505, + 429 + ], + "score": 1.0, + "content": "to stop). It also had a high level of under-generation as measured by WDR, typically due to early", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 428, + 506, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 506, + 441 + ], + "score": 1.0, + "content": "cutoff. Tacotron 2 (GMMA) performed almost as well as the supervised Non-Attentive Tacotron in", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 437, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 506, + 452 + ], + "score": 1.0, + "content": "WDR because of its soft monotonic nature, which made end-of-sentence prediction easier. However,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 449, + 506, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 506, + 462 + ], + "score": 1.0, + "content": "it still had significantly higher level of over-generation compared to Non-Attentive Tacotron, even", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 460, + 506, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 506, + 473 + ], + "score": 1.0, + "content": "when unsupervised or semi-supervised duration modeling is used for the latter. The robustness of", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 471, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 505, + 484 + ], + "score": 1.0, + "content": "semi-supervised and unsupervised Non-Attentive Tacotron is significantly worse than the supervised", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 481, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 505, + 496 + ], + "score": 1.0, + "content": "one. Manual investigation uncovered that the typical failure pattern is that part of the spectrogram", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 493, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 505, + 506 + ], + "score": 1.0, + "content": "is not correctly synthesized (often as silence, but sometimes as babbling), despite that the duration", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 504, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 505, + 516 + ], + "score": 1.0, + "content": "prediction seems reasonable. Such failure pattern contributes to both UDR and WDR. This indicates", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 515, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 505, + 528 + ], + "score": 1.0, + "content": "further improvements to be made. Even then, the semi-supervised and unsupervised Non-Attentive", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 525, + 454, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 454, + 539 + ], + "score": 1.0, + "content": "Tacotron still performs significantly better on over-generation compared to Tacotron 2.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 108, + 543, + 505, + 587 + ], + "lines": [ + { + "bbox": [ + 105, + 542, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 505, + 556 + ], + "score": 1.0, + "content": "In practice, we also observed that Tacotron 2 required significantly more care in data preprocessing", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 554, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 554, + 505, + 567 + ], + "score": 1.0, + "content": "to achieve this level of robustness, including consistent trimming of leading and trailing silences and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 564, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 505, + 578 + ], + "score": 1.0, + "content": "filtering out utterances with long pauses. 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SystemLibriTTSweb-long
UDR (%)WDR (%)UDR (%)WDR (%)
Tacotron 2
w/LSA16.960.446.044.4
w/ GMMA3.8120.16.1571.3
Non-Attentive Tacotron
Supervised0.0050.10.0111.1
Semi-supervised0.2660.90.6953.5
Unsupervised0.2230.70.5273.2
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Tacotron 2 (LSA)", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 395, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 106, + 395, + 506, + 408 + ], + "score": 1.0, + "content": "suffered from severe over-generation as measured by UDR, especially on long inputs. Manual", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 405, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 505, + 419 + ], + "score": 1.0, + "content": "investigation uncovered that they were typically long babbling or long silence, often at the end (failure", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 417, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 505, + 429 + ], + "score": 1.0, + "content": "to stop). It also had a high level of under-generation as measured by WDR, typically due to early", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 428, + 506, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 506, + 441 + ], + "score": 1.0, + "content": "cutoff. Tacotron 2 (GMMA) performed almost as well as the supervised Non-Attentive Tacotron in", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 437, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 506, + 452 + ], + "score": 1.0, + "content": "WDR because of its soft monotonic nature, which made end-of-sentence prediction easier. However,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 449, + 506, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 506, + 462 + ], + "score": 1.0, + "content": "it still had significantly higher level of over-generation compared to Non-Attentive Tacotron, even", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 460, + 506, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 506, + 473 + ], + "score": 1.0, + "content": "when unsupervised or semi-supervised duration modeling is used for the latter. The robustness of", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 471, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 505, + 484 + ], + "score": 1.0, + "content": "semi-supervised and unsupervised Non-Attentive Tacotron is significantly worse than the supervised", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 481, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 505, + 496 + ], + "score": 1.0, + "content": "one. Manual investigation uncovered that the typical failure pattern is that part of the spectrogram", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 493, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 505, + 506 + ], + "score": 1.0, + "content": "is not correctly synthesized (often as silence, but sometimes as babbling), despite that the duration", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 504, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 505, + 516 + ], + "score": 1.0, + "content": "prediction seems reasonable. Such failure pattern contributes to both UDR and WDR. This indicates", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 515, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 505, + 528 + ], + "score": 1.0, + "content": "further improvements to be made. Even then, the semi-supervised and unsupervised Non-Attentive", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 525, + 454, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 454, + 539 + ], + "score": 1.0, + "content": "Tacotron still performs significantly better on over-generation compared to Tacotron 2.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 383, + 506, + 539 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 543, + 505, + 587 + ], + "lines": [ + { + "bbox": [ + 105, + 542, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 505, + 556 + ], + "score": 1.0, + "content": "In practice, we also observed that Tacotron 2 required significantly more care in data preprocessing", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 554, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 554, + 505, + 567 + ], + "score": 1.0, + "content": "to achieve this level of robustness, including consistent trimming of leading and trailing silences and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 564, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 505, + 578 + ], + "score": 1.0, + "content": "filtering out utterances with long pauses. On the other hand, Non-Attentive Tacotron is significantly", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 576, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 287, + 589 + ], + "score": 1.0, + "content": "less sensitive to the data preprocessing steps.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 542, + 505, + 589 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 613, + 201, + 626 + ], + "lines": [ + { + "bbox": [ + 104, + 611, + 203, + 629 + ], + "spans": [ + { + "bbox": [ + 104, + 611, + 203, + 629 + ], + "score": 1.0, + "content": "7 CONCLUSIONS", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 644, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 656 + ], + "score": 1.0, + "content": "This paper presented Non-Attentive Tacotron, showing a significant improvement in robustness", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "compared to Tacotron 2 as measured by unaligned duration ratio and word deletion rate, while also", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "slightly outperforming it in naturalness. This was achieved by replacing the attention mechanism", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "in Tacotron 2 with an explicit duration predictor and Gaussian upsampling. We demonstrated the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "ability to control the pacing of the entire utterance as well as individual words using the duration", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "score": 1.0, + "content": "predictor. 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FVAE
Yes
512×2
5×1
512 64
Mel spectrogram dynamic range compressionlog(x +0.001)
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Speaker embedding dim
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Segment encoder conv dim[512,512,512]
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Layer norm attention inputs
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Duration PredictorBi-LSTM dim512×2
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Xdur supervised2.0
Xdur semi-supervised100.0
100.0
Au semi-supervised1×10-3
XKL semi-supervised
Xu unsupervised1.0
Range Parameter Predictor入KL unsupervised1 ×10-4
Bi-LSTM dim512×2
Positional EmbeddingProjection activationSoftPlus
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Timestep denominator10.000
Decoder[256,256]
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[0.5,0.5]
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FVAE
Yes
512×2
5×1
512 64
Mel spectrogram dynamic range compressionlog(x +0.001)
Token embedding dim
Speaker embedding dim
Conv kernel
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Conv batch norm decay0.999
Bi-LSTM dim
Segment encoder conv kernel3×1
Segment encoder conv dim[512,512,512]
Segment encoder Bi-LSTM dim256×2
Layer norm attention inputs
Latent dim8 projected to 16
Duration PredictorBi-LSTM dim512×2
Projection activationNone
Xdur supervised2.0
Xdur semi-supervised100.0
100.0
Au semi-supervised1×10-3
XKL semi-supervised
Xu unsupervised1.0
Range Parameter Predictor入KL unsupervised1 ×10-4
Bi-LSTM dim512×2
Positional EmbeddingProjection activationSoftPlus
Embedding dim32
Timestep denominator10.000
Decoder[256,256]
Pre-net dim supervised
Pre-net dim semi/unsupervised[128,128]
Pre-net activation[ReLU,ReLU]
[0.5,0.5]
Pre-net dropout prob
LSTM dim^1,024
LSTM inituniform(0.1)
Projection inituniform(0.1)
Post-net conv kernel5×1
Post-net conv dim
[512,512,512,512,128]
Post-net conv activation
[tanh,tanh,tanh,tanh,None]
Post-net conv init
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WERdelinssubWERdelinssub
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Char2Wav2017
Tacotron2017
Deep Voice 22017
Tacotron 22018
Deep Voice 32018
Transformer TTS2019
CHiVE2019
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SystemLibriTTSweb-long
WERdelinssubWERdelinssub
Tacotron 2
w/LSA1.80.40.31.113.04.42.06.7
w/ GMMA1.70.10.11.510.11.31.37.4
Non-Attentive Tacotron
Supervised1.40.10.11.29.31.11.36.9
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Unsupervised3.50.70.32.615.33.22.010.1
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ModelMOS
Tacotron 2
w/LSA4.35 ± 0.05
w/ GMMA4.37 ± 0.04
Non-Attentive Tacotron w/ Gauss. upsampling
w/ vanilla upsampling4.41 ± 0.04
4.13 ± 0.05
Ground truth4.42 ± 0.04
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TrainingModelDur. MAE (ms)MOS
Unsupervisedw/o FVAE124.42.91± 0.09
w/ FVAE41.34.31 ± 0.04
Semi-supervisedw/o FVAE21.54.19 ± 0.05
Supervisedw/FVAE18.34.35 ± 0.04
Non-Attentive Tacotron15.44.37 ± 0.04
Tacotron2 w/ GMMA-4.35 ± 0.04
Ground truth=4.52 ± 0.03
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SystemLibriTTSweb-long
UDR (%)WDR (%)UDR (%)WDR (%)
Tacotron 2
w/LSA16.960.446.044.4
w/ GMMA3.8120.16.1571.3
Non-Attentive Tacotron
Supervised0.0050.10.0111.1
Semi-supervised0.2660.90.6953.5
Unsupervised0.2230.70.5273.2
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CommonTraining modeSynchronous 32
Batch size (per replica) Replicas Parameter init L² regularization Learning rate Learning rate scheduleXavier 1 ×10-6 0.001
Inputs and TargetsOptimizer LSTM zone-out prob LSTM cell abs value cap Sampling rate (Hz) Normalize waveform Pre-emphasis Frame size (ms) Frame hop (ms)decay half every 50K steps. Adam(0.9,0.999,1 × 10-6) 0.1 10.0 24,000 No No 50
EncoderMel channels K Mel frequency lower bound (Hz) Mel frequency upper bound (Hz)128 20 12,000
FVAE
Yes
512×2
5×1
512 64
Mel spectrogram dynamic range compressionlog(x +0.001)
Token embedding dim
Speaker embedding dim
Conv kernel
Conv dim[512, 512, 512]
Conv activation[None,None,None]
Conv batch norm decay0.999
Bi-LSTM dim
Segment encoder conv kernel3×1
Segment encoder conv dim[512,512,512]
Segment encoder Bi-LSTM dim256×2
Layer norm attention inputs
Latent dim8 projected to 16
Duration PredictorBi-LSTM dim512×2
Projection activationNone
Xdur supervised2.0
Xdur semi-supervised100.0
100.0
Au semi-supervised1×10-3
XKL semi-supervised
Xu unsupervised1.0
Range Parameter Predictor入KL unsupervised1 ×10-4
Bi-LSTM dim512×2
Positional EmbeddingProjection activationSoftPlus
Embedding dim32
Timestep denominator10.000
Decoder[256,256]
Pre-net dim supervised
Pre-net dim semi/unsupervised[128,128]
Pre-net activation[ReLU,ReLU]
[0.5,0.5]
Pre-net dropout prob
LSTM dim^1,024
LSTM inituniform(0.1)
Projection inituniform(0.1)
Post-net conv kernel5×1
Post-net conv dim
[512,512,512,512,128]
Post-net conv activation
[tanh,tanh,tanh,tanh,None]
Post-net conv init
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SystemLibriTTSweb-long
WERdelinssubWERdelinssub
Tacotron 2
w/LSA1.80.40.31.113.04.42.06.7
w/ GMMA1.70.10.11.510.11.31.37.4
Non-Attentive Tacotron
Supervised1.40.10.11.29.31.11.36.9
Semi-supervised3.30.90.22.214.13.51.69.0
Unsupervised3.50.70.32.615.33.22.010.1
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ModelYearARFFRNNTransformerFull ConvAttentionDuration
Deep Voice2017
Char2Wav2017
Tacotron2017
Deep Voice 22017
Tacotron 22018
Deep Voice 32018
Transformer TTS2019
CHiVE2019
DurIAN2019
Fastspeech2019
TalkNet2020
AlignTTS2020
JDI-T2020
Non-Attentive Tacotron2020
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b/parse/train/JG-SlCAx5_K/JG-SlCAx5_K.md new file mode 100644 index 0000000000000000000000000000000000000000..30b610693f63594e8c7a0c85dd54ee62d657d7aa --- /dev/null +++ b/parse/train/JG-SlCAx5_K/JG-SlCAx5_K.md @@ -0,0 +1,305 @@ +# Geometry Processing with Neural Fields + +Guandao Yang ∗ Cornell University + +Serge Belongie University of Copenhagen + +Bharath Hariharan Cornell University + +Vladlen Koltun Intel Labs + +# Abstract + +Most existing geometry processing algorithms use meshes as the default shape representation. Manipulating meshes, however, requires one to maintain high quality in the surface discretization. For example, changing the topology of a mesh usually requires additional procedures such as remeshing. This paper instead proposes the use of neural fields for geometry processing. Neural fields can compactly store complicated shapes without spatial discretization. Moreover, neural fields are infinitely differentiable, which allows them to be optimized for objectives that involve higher-order derivatives. This raises the question: can geometry processing be done entirely using neural fields? We introduce loss functions and architectures to show that some of the most challenging geometry processing tasks, such as deformation and filtering, can be done with neural fields. Experimental results show that our methods are on par with the well-established mesh-based methods without committing to a particular surface discretization. Code is available at https://github.com/stevenygd/NFGP. + +# 1 Introduction + +In many graphics applications, users may want to edit digital shapes using just a few clicks, such as making a character bow by dragging the head downwards. Such manipulation from sparse input requires geometry processing algorithms. Most of these algorithms use polygonal meshes to represent shapes [11]. Polygonal meshes were created initially for researchers as a representation of real-world shapes that they can both interpret and manipulate [14, 52, 78]. However, developing algorithms that automatically manipulate meshes is often difficult since they involve discretizing the surface. For example, changing the topology of a mesh, such as turning a sphere into a torus, will break such discretization and require additional repair procedures such as remeshing [2, 3]. Given that shape editing is increasingly performed by algorithms, it seems worthwhile to search for a shape representation that is more amenable to automatic geometry processing. + +An alternative to the polygonal mesh is an implicit representation, in which the surface is represented by a level set of a field: $\bar { \{ x \vert f ( x ) = c \} }$ [22, 39, 63]. Since it is easy to change shape topology using implicit representations, people have applied them for geometry processing tasks such as shape merging [8, 51, 54]. These works store implicit fields using voxels or octrees, which introduce memory-intensive spatial discretization. Recent research addresses this by using continuous neural networks to represent implicit fields [19, 45, 46, 56]. These neural fields possess several advantages in addition to the merits inherited from implicit representation: they are compact to store [23, 45] and can produce high-quality continuous surfaces at arbitrary resolutions [45, 56]. The community has achieved compelling results using neural fields in a variety of applications [47, 64, 73, 84]. Notwithstanding these results, it is still unclear whether shape editing tasks challenging for implicit fields (e.g., deformation and filtering) can be performed with neural fields. In this paper, we ask: can geometry processing be done entirely using neural fields? + +Geometry processing tasks are challenging because they are typically under-constrained: user input is very sparse. Therefore, we need to leverage priors that characterize how a natural surface behaves. Such surface priors are usually instantiated by minimizing energy functionals that describe the physical properties of surfaces using operators from differential geometry. For example, one can encourage surfaces to be smooth by minimizing the curvature, which can be measured by the LaplaceBeltrami operator. Such operators, however, require a parameterization of the surface, which is not available for level sets of a neural field. Mesh algorithms usually approximate these geometric operators using the geodesic neighbors of the surface point. This allows the algorithms to focus on intrinsic geometric properties that are independent of shape parameterization. However, it is not easy to obtain geodesic neighbors in a neural field since the surface of interest is encoded implicitly by a set of points that evaluate the field function to the same value. + +We posit that computing these geometric operators in neural fields requires a fundamentally different approach. The idea is to approximate the local surface of the level set using the derivatives of the underlying field. We can evaluate intrinsic geometry properties of the level set, such as curvature, using only the field derivatives [39, 54]. This allows us to develop loss functions that describe surface priors such as elasticity or rigidity. To achieve this, we use the fact that neural fields are designed to be infinitely differentiable [66, 74]. The infinite differentiability of neural fields makes it possible to optimize loss functions that involve higher-order derivatives using gradient descent methods. Thus, unlike mesh-based geometry processing algorithms that approximate these objectives using surface discretizations, we can directly optimize in terms of the derivatives of the field. + +Our formulation provides a proof of concept that geometry processing can be done entirely using neural fields. In particular, we focus on two tasks: shape filtering (e.g., smoothing and sharpening) and topology-preserving deformations. These two tasks are not only essential for downstream applications but also bring out the known challenges associated with implicit representations. We first tackle shape sharpening and smoothing and show how these can be done by optimizing a loss function based on geometric properties computed via the neural field’s derivatives. To achieve shape deformation, we propose to warp the neural field using a deformation vector field modeled by an invertible neural network [7]. With this invertible deformation field, we derive a training objective that models the implicitly represented surfaces as elastic shells. + +We compare our method with well-established mesh-based baselines [70, 76]. Our method can match the quality of the mesh-based counterparts without discretizing the surface. We hope that our work can inspire future generations of geometry processing algorithms using neural fields. + +# 2 Related Work + +This paper builds on two bodies of work: polygon mesh geometry processing and neural field representations. We will focus on prior work on two geometry processing tasks: shape filtering and topology-preserving deformation. Please refer to Botsch et al. [11] for further reading. + +Mesh smoothing (and sharpening). The goal of mesh smoothing is to remove high-frequency noise and produce a smooth surface. Noise removal can be achieved by Fourier analysis [76, 79] or by modeling surface motion with a diffusion equation [26]. Smoothness can be promoted by minimizing energy functionals inspired by differential operators [50, 72, 82]. Sharpening is the inverse of smoothing. In this paper, we adopt the goal of smoothing from prior work [20, 76] and design a corresponding differentiable objective for neural fields. + +Implicit field smoothing. Implicit representations can be smoothed by evolving the level set according to its curvature normal [49, 54]. Many network architectures, such as ReLU MLP, bias toward smoothness when modeling an implicit field [61, 66, 74]. Regularization objectives and initialization schemes have been proposed to obtain smooth level sets from scanned surface points [5, 31]. These works mostly use smoothness as a prior when training neural fields. Our work formulates an objective that allows smoothing or sharpening a neural field as desired. + +Mesh deformation. Mesh deformation is done by either deforming the shape (i.e. vertices) [9, 69] or the space [6, 36, 41, 48, 65]. These algorithms usually draw inspiration from physics and differential geometry to develop energy functions that encourage natural deformation [10, 15, 24, 70, 71, 77]. They also linearize such objectives so that they can be solved efficiently using linear solvers [9]. Recent research also applies deep learning to optimize for non-linear deformation losses [32, 34, 38, 80, 81, 83]. Deforming a mesh, however, requires estimating the deformation objectives with spatial discretization and maintaining vertex connectivity in a way that preserves topology [42]. We deform neural fields with a continuous invertible field to circumvent these issues. + +Implicit field deformation. Prior works have studied the deformation of implicit fields for tasks like physics simulation [39, 51, 54, 55]. These works use voxels or octrees to represent implicit fields, while our paper advocates for using neural fields for deformation. There is some past work on deforming neural fields to match a target shape [12, 18, 37, 53, 58] or image [43, 57, 60] without any correspondences between the two. In contrast, we perform such deformation with very few localized user-provided correspondences, but without any other information about the target shape. Our setting is very convenient for artists, but it requires the algorithm to provide a strong surface prior due to the lack of a densely specified target state. Other prior works on editing neural fields are trained on a dataset of shapes from a particular object category [25, 29, 30, 33, 85]. Since surface priors are specified implicitly by the dataset, it is unclear how to apply these methods to out-of-distribution shapes. In contrast, our paper requires no training dataset and instead enforces priors inspired by more general physical properties such as smoothness and elasticity. Remelli et al. [62] developed a way to differentiate iso-surface extraction, which allows deforming neural fields using objectives carried over from mesh-based algorithms. Our method avoids iso-surface extraction entirely and formulates differentiable deformation objectives directly on the implicit field. + +# 3 Computing Surface Properties of Neural Fields + +In this section, we will discuss how to compute surface properties using neural fields and establish notation for the following sections. Let $\partial \Omega$ be a surface enclosing the region $\Omega$ . A signed distance field (SDF) for surface $\partial \Omega$ is defined as $d ( \mathbf { x } ) = s ( \mathbf { x } ) \operatorname* { m i n } _ { \mathbf { y } \in \partial \Omega } \bar { \| } \mathbf { x } - \mathbf { y } \bar { \| }$ . The sign function $s ( \mathbf { x } )$ evaluates to $- 1$ if $\textbf { x } \in { \Omega }$ and 1 otherwise. We will assume that a neural field approximate an SDF whose zero-isosurface represents the surface of interest. For a neural field $f$ , we denote its zero-isosurface using $\mathcal { M } _ { f }$ . This section summarizes how to compute surface normals and curvatures from neural fields. This is well-understood and we summarize this here for convenience [39, 54, 59]. + +Surface normal. The surface normal is the vector perpendicular to the tangent plane and describes the local orientation of the surface. For an SDF, the outward oriented surface normal of its level set is the field gradient: $\mathbf { n } _ { d } ( \mathbf { x } ) = \nabla _ { \mathbf { x } } d ( \mathbf { x } )$ . It can be shown that the SDF’s gradient norm is always one: $\lVert \nabla _ { \mathbf { x } } d ( \mathbf { x } ) \rVert = 1$ . This property can be used to ensure that the field remains a valid SDF throughout any manipulation [4, 31]. The closest point in $\partial \Omega$ from $\mathbf { x }$ can be found by $\mathbf { x } - d ( \mathbf { x } ) \mathbf { n } _ { d } ( \mathbf { x } )$ . This property can be used to sample points from the isosurface without creating a mesh [5, 13]. Finally, since the tangent plane is perpendicular to the surface normal, we can project vectors onto the tangent plane by subtracting their projection onto the normal using the following projection matrix $\mathbf { x }$ : $\mathbf { P } _ { d } \mathbf { \bar { ( x ) } } \overset { \mathbf { \bar { \alpha } } } { = } \mathbf { I } - \mathbf { \bar { n _ { d } } } \mathbf { ( x ) } \mathbf { n } _ { d } \mathbf { ( x ) } \mathbf { \breve { \alpha } }$ . This projection matrix allows us to characterize the tangent plane. This matrix is important for measuring how much a given deformation stretches the tangent direction [35]. + +Curvature. Intuitively, curvature describes how much a surface deviates from a plane. This can be captured by the total derivative of the surface normal, which is also known as the shape operator: $\bar { \mathbf { \xi } } S _ { D } ( \bar { \mathbf { x } } ) = \mathcal { D } \bar { \mathbf { n } _ { d } } ( \mathbf { x } )$ . For an SDF, the normal itself is given by the derivative of the field, thus the shape operator for an SDF is the Hessian of the field function: $\dot { H _ { d } } ( \mathbf { x } ) = \mathcal { D } ^ { 2 } d ( \mathbf { x } )$ . The shape operator can be used to capture many different notions of curvature, including mean curvature (half the trace of $S _ { D } ( \mathbf { x } )$ , denoted by $\bar { \kappa }$ ), Gaussian curvature (the determinant of $S _ { D } ( { \bf x } ) _ { , }$ ), and principal curvatures (the eigenvalues of $S _ { D } ( { \bf x } ) _ { , }$ ). We will use these to define objectives that smooth or sharpen the surface. + +# 4 Shape Smoothing and Sharpening + +In this section, we will show that shape smoothing and sharpening can be done directly on neural fields without producing meshes. In our setup, the input shape is represented as the zero-isosurface $\mathcal { M } _ { F }$ of the neural field $F$ . The algorithm needs to output neural field $G _ { \theta }$ whose zero-isosurface $\mathcal { M } _ { G _ { \theta } }$ satisfies two goals. First, $\mathcal { M } _ { G _ { \theta } }$ should preserve the global structure of $\mathcal { M } _ { F }$ . Second, the surface $\mathcal { M } _ { G _ { \theta } }$ should make desired changes to match the curvature of shape $\mathcal { M } _ { F }$ . + +![](images/a582fb6a973a707da2ca642467983ef490d9b46ef69834159125364e1493a4b2.jpg) +Figure 2: Smoothing and sharpening results. (A) zoomed-in input; (B) our method; (C) baseline without remeshing; (D) baseline with remeshing. We can see that the baseline without remeshing finds it difficult to smooth or sharpen the mesh extracted from neural fields. Our method is able to achieve good results without discretizing the surface. + +To achieve these goals, we first instantiate $G _ { \theta }$ using the same architecture and parameter values as $F$ Then we optimize $G _ { \theta }$ using the following objective: + +$$ +\mathcal { L } ( \theta ) = \int _ { \mathbf { x } \in U } \left| G _ { \theta } ( \mathbf { x } ) - F ( \mathbf { x } ) \right| ^ { 2 } + \lambda _ { g } \left( \left\| \nabla _ { \mathbf { x } } G _ { \theta } ( \mathbf { x } ) \right\| - 1 \right) ^ { 2 } d \mathbf { x } + \int _ { \mathbf { x } \in V _ { \tau } } \lambda _ { k } \left( \kappa _ { G _ { \theta } } ( \mathbf { x } ) - \beta \kappa _ { F } ( \mathbf { x } ) \right) ^ { 2 } d \mathbf { x } . +$$ + +The first integral encourages the network $G _ { \theta }$ to preserve the original shape. The second term regularizes $G _ { \theta }$ to remain a valid SDF by enforcing that the norm of the gradient is 1 (i.e., the Eikonal constraint [4, 31]). The integration is over the region $U$ where the original neural field $F$ is supervised over. The final term aims to smooth or sharpen the surface by increasing or decreasing the curvature $\kappa$ . Setting $\beta < 1$ will decrease the curvature of the output surface $\kappa _ { G _ { \theta } }$ , resulting in a smoother shape. $\beta > 1$ will lead to surfaces with higher curvature details and will thus sharpen shapes. In this paper, we will use mean curvature since it’s easy to compute with neural fields: $\kappa _ { f } ( \mathbf { x } ) = \mathrm { t r } \mathcal { D } ( \mathbf { n } _ { f } ( \mathbf { x } ) )$ . + +![](images/f46db6fa8fd3ad41d2bd57bfbf0b5032fd160bdb630f47e8f74bab8da49662dd.jpg) +Figure 1: L: SIREN learned to fit the SDF of a square; R: Zooming in on the surface. + +One challenge is that the computation of curvature can be very noisy for neural fields using periodic activations. Figure 4 shows how an ostensibly smooth isosurface learned through SIREN [66] is actually quite rough when zoomed in. The curvature evaluated on such a rough surface can be too noisy to be used for training. To alleviate this issue, we only compute the curvature regularization in areas where the curvature of the level set is less than a certain threshold $\tau$ . Formally, we define this area as $V _ { \tau } = \{ \mathbf { x } \in U | \operatorname* { m a x } ( | \kappa _ { G _ { \theta } } | , | \kappa _ { F } | ) < \tau \}$ . We use rejection sampling to sample points from $V _ { \tau }$ when computing the loss during training. + +Results. We follow prior works [20, 76] to use Armadillo [40] and a sphere with one half of it corrupted by Gaussian noise. We compare our algorithm to two baselines. The first baseline directly applies the smoothing algorithm developed by Taubin [76] to the mesh extracted from the neural field using Marching cube [44]. The second baseline applies the filtering algorithms on meshes simplified by quadratic decimation [27]. The input neural fields are created following the procedure of Park et al. [56]. The results are shown in Figure 2. The first baseline fails to smooth or sharpen the surface appropriately. It only modifies the surface with high-frequency noise. While the second baseline can filter the surface correctly, it introduces discretization artifacts due to the decimation process. This suggests it is challenging to filter the neural field surface with mesh processing algorithms since these algorithms are sensitive to the quality of surface discretization. On the other hand, our algorithm can produce good filtering results without the need to maintain a good discretization of the surface. + +# 5 Deformation + +To deform a shape, the user will choose a set of deformation handles $\{ { \bf h } _ { i } \} _ { i = 1 } ^ { n }$ . For each handles $\mathbf { h } _ { i }$ , the user will specify a target location $\mathbf { t } _ { i }$ describing where the handle will be dragged to. Users can set $\mathbf { t } _ { i } = \mathbf { h } _ { i }$ to enforce a part of the surface to be unchanged. Given this input, there are two goals for the shape deformation algorithm: 1) satisfying user inputs and 2) ensuring that the deformation resembles the natural behavior of real objects. The input shape will be represented by the zero-isosurface of a neural field $F$ in our setting. The algorithm must therefore output a neural field $G _ { \theta }$ whose zero-isosurface represents the deformed shape that satisfies the aforementioned two goals. + +In this setting, deformation can be formulated as solving a constrained optimization problem: + +$$ +\operatorname* { m i n } _ { \theta } \ \mathcal { L } _ { d f m } ( G _ { \theta } , F ) \quad \mathrm { s . t . } \ \mathcal { L } _ { c o n s t } ( G _ { \theta } , \mathbf { t } _ { i } , \mathbf { h } _ { i } ) = 0 , 1 \leq i \leq n , +$$ + +where the objective $\mathcal { L } _ { d f m } ( G _ { \theta } , F )$ measures how natural the deformation is. The constraints $\mathcal { L } _ { c o n s t } ( G _ { \theta } , \mathbf { t } _ { i } , \mathbf { h } _ { i } ) = 0$ ensure that the result deformation matches user input. + +One way to ensure a natural-looking deformation is to assume that the surface behaves like a thin elastic shell, which is resistant to stretching and bending [1, 70]. Traditional mesh-based algorithms model elasticity by minimizing the thin shell energy that penalizes stretching or bending happened to any local patch. Naively adapting such training objectives from mesh-based algorithms to neural fields is challenging because these algorithms assume dense correspondences between two surfaces and efficient access to geodesic neighbors. + +In this section, we will address these challenges by following strategy. To measure how much bending or stretching happened to the whole surface, we will first divide the surface into infinitesimal patches and then sum the amount of bending or stretching that happened to each patch. To achieve that, we first develop a sampling schema to sample these infinitesimal patches uniformly from the input shapes (Sec 5.1). Then we warp the input shape with an invertible neural network to achieve correspondences between the input and output surfaces (Sec 5.2). Finally, we derive ways that measure the amount of bending and stretching between two infinitesimal surface patches (Sec 5.3). + +# 5.1 Sampling + +Our first step is to sample infinitesimal surface patches uniformly to the surface area from the zero-isosurface of the neural field. Each infinitesimal surface patch can be represented by a surface point and its local derivatives. With this said, the problem amounts to sampling points from the zero-isosurface. Formally, we are given a neural field $F$ that approximates the signed distance field of the input shape. The goal is to find a way to sample an arbitrary number of points on its zero-isosurface $\mathcal { M } _ { F }$ . One way to sample points from $\mathcal { M } _ { F }$ is to run Langevin dynamics using the gradient of the field $F$ [5, 13]: $\mathbf { x } _ { t + 1 } \overset { \cdot } { = } \tilde { \mathbf { x } } _ { t } - F ( \tilde { \mathbf { x } } _ { t } ) n _ { F } ( \tilde { \mathbf { x } } _ { t } )$ , $\tilde { \mathbf { x } } _ { t } \sim \mathcal { N } ( \mathbf { x } _ { t } , \sigma \mathbf { I } )$ . $\mathbf { x } _ { \mathrm { 0 } }$ are initialized by sampling uniformly within $[ - 1 , 1 ] ^ { 3 }$ . Here we also leverage an SDF property: the closest surface point to $\mathbf { x }$ can be computed by ${ \bf x } - { \bf n } ( { \bf x } ) F ( { \bf x } )$ (Sec 3). While this process produces points guaranteed to be on the zero-isosurface, the mixing time of the procedure is very long without appropriate coarse-to-fine annealing [68]. Running this process for limited iterations results in point samples that are concentrating near the high curvature area, as shown on the left side of Figure 5.1. + +![](images/1bb5cd9809445b92975f25d3de02307121f0571a65d61bf8b055406cdc447ce9.jpg) +Figure 3: Sampling from dino. L: no rejection; R: ours (with rejection). + +To alleviate this issue, we instantiate the sampling procedure with $\mathbf { x } _ { \mathrm { 0 } }$ sampled from a rough shape. This can be done by first sampling uniformly from the bounded space and rejecting points that are too far away from the isosurface: $\mathbf { x } _ { 0 } \sim \{ \mathbf { x } \in U ( - 1 , 1 ) | F ( \mathbf { x } ) < \tau _ { s } \}$ . We found that $\tau _ { s }$ can be set to a relatively large number (e.g., about 0.1). This prevents high rejection rates without sacrificing sampling quality. Figure 5.1 shows that our method creates uniform samples. + +We quantitatively evaluate the effectiveness of the sampling scheme. Specifically, we compare our sampling scheme with directly applying Langevin dynamics [13] ( $L D$ in Table 1). To do that, we compute the Chamfer Distance (CD) and Earth Mover Distance (EMD) between points sampled by the valuated algorithms and points sampled uniformly from the extracted mesh. For both metrics, lower values indicate better performance Since larger surfaces can lead to larger CD and EMD values, we normalize the metrics by the values obtained by comparing two sets of uniform samples from the mesh (i.e., CDr and EMDr) The results show that initializing $\mathbf { x } _ { \mathrm { 0 } }$ by rejection sampling significantly improves both CD and EMD compared to naively applying Langevin dynamics, at a minor cost in sampling time. + +# 5.2 Invertible Deformation Field + +After we obtained surface points samples from zero isosurfaces of the input neural fields, the next step is to deform these surface points to the output shapes. One way to deform neural fields is to warp the coordinate space of the input network using a deformation field predicted by a neural network $D _ { \theta }$ [25, 43, 57]. Under this framework, the output network can be defined as $G _ { \theta } ( \mathbf { x } ) = F ( D _ { \theta } ( \mathbf { x } ) )$ . Then the constraint $\mathcal { L } _ { c o n s t } ( G _ { \theta } , \mathbf { t } , \mathbf { h } )$ can be defined as $\mathcal { L } _ { c o n s t } ( G _ { \theta } , \mathbf { t } , \mathbf { h } ) = \| D _ { \theta } ( \mathbf { t } ) - \mathbf { h } \|$ . + +Table 1: Our sampling method achieves better results than the baseline. + +
Dino Armadillo
MetricsLDOursLDOurs
CDr (↓)1.541.041.361.02
EMDr (↓)3.381.153.301.08
Time0.150.210.120.18
+ +Ideally, we would like the deformation $D _ { \theta }$ to be continuous and invertible. This will allow us to create well-behaved one-to-one correspondences between points on the deform shape (i.e., x) and points on the input shape (i.e., $D _ { \theta } ( \mathbf { x } ) )$ . To achieve this, we make $D _ { \theta }$ to be an invertible network composed of a sequence of invertible residual blocks [7]. + +Invertible residual block. Prior works [7, 17] have shown that a sufficient condition for the residual block $f ( x ) = x + g ( x )$ to be invertible is that the Lipschitz constant of function $g$ is less than 1. The architecture of the network $g ( x )$ is usually composed of spectral normalized linear layers and Lipschitz continuous nonlinearities such as ELU [21]. The inverse of such residual block can be computed by finding the fixed point of function $y \mapsto y - g ( x )$ [7]. Intuitively, deforming using one invertible residual block amounts to moving point $x$ with deformation vector $g ( x )$ . + +Lipschitz continuous positional encoding. Applying such architecture directly without modification fails to produce deformations with many different local rotations. Recent research suggests that periodic functions are essential for coordinate MLPs to predict complex signals [47, 66, 74]. Periodic functions are usually used as positional encoding or activations of the form $\sin ( a x + b )$ , where $a$ controls the frequency of the activation. To use such periodic function as part of the invertible residual block without restricting the frequency, we normalize the output of the periodic function $\sin ( a x + b ) | a | ^ { - 1 }$ , bringing it is Lipschitz constant below 1. Formally, the positional encoding with normalized Lipschitz constant applied to one dimension is + +$$ +\gamma _ { i } ( { \bf x } ) = \frac { 1 } { \sqrt { 2 L + 1 } } \left( x _ { i } , \frac { \cos ( 2 ^ { 0 } \pi { \bf x } _ { i } ) } { 2 ^ { 0 } \pi } , \frac { \sin ( 2 ^ { 0 } \pi { \bf x } _ { i } ) } { 2 ^ { 0 } \pi } , \ldots , \frac { \cos ( 2 ^ { L } \pi { \bf x } _ { i } ) } { 2 ^ { L } \pi } , \frac { \sin ( 2 ^ { L } \pi { \bf x } _ { i } ) } { 2 ^ { L } \pi } \right) . +$$ + +We will apply such encoding to each of the dimensions of the input coordinate for the body of the invertible residual block: $\begin{array} { r } { \bar { R _ { \theta } } ( \mathbf { x } ) = \mathbf { x } + g _ { \theta } \left( \frac { 1 } { \sqrt { d } } [ \gamma _ { 1 } \left( \mathbf { x } \right) , \mathbf { \Omega } , \mathbf { \Omega } . . . , \gamma _ { d } \left( \mathbf { \bar { x } } \right) ] \right) } \end{array}$ . + +Ablation. We conduct ablation studies on two architecture choices: invertibility and positional encoding. In this experiment, we deform a neural field representing the SDF of a 2D rectangle. We optimize each ablation case to satisfies the user specified constraints with following loss: $\begin{array} { r } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left\| D _ { \theta } ( \mathbf { h } _ { i } ) - \mathbf { t } _ { i } \right\| ^ { 2 } } \end{array}$ . The results are shown in Figure 4. If we replace the invertible architecture with SIREN as done in Deng et al. [25], the deformation field will tend to break topology (No inverse). Removing the positional encoding will fail to create a complex field (No $P E _ { \mathrm { { \ell } } }$ ). Our architecture can create a reasonable guess (No loss). This shows that our network architecture prioritizes natural deformation that preserves topology. + +![](images/513a5400ffef192f910dfe03539db2c361a75645844fec54771cf23c63e7d2b7.jpg) +Figure 4: Architecture ablation on 2D SDF deformation. Blue points are handles; Red points are targets. + +# 5.3 Implicit Thin Shell Loss + +At this point, we have obtained the correspondences $\mathbf { y } = D _ { \theta } ( \mathbf { x } )$ , with $\mathbf { x }$ in the output (or deformed) space and y in the input space. Our next step is to design $\mathcal { L } _ { d f m }$ that compares these corresponding patches to ensure natural deformation. Recall that one way to ensure a natural-looking deformation is to minimize the amount the resistance to bending or stretching that happened during the deformation [1, 70]. We will develop novel loss functions for measuring stretching and bending. Please refer to the supplement for the connection between our loss and the thin shell energy. + +# 5.3.1 Stretching Loss + +Stretching can be captured by the change of dot product in tangent space. Intuitively, a local surface patch is stretched when the lengths of some tangent vectors change. The change of tangent vectors’ norm can be measured by the tangent dot-product. With this said, the amount of stretch can be measured by the change of tangent dot product. + +Note that we do not have access to analytical surface parameterization, so we need to express the tangent dot product with neural fields and its derivative. We can describe the tangent dot product to the spatial dot product using the projection matrix. The tangent vector of $\mathbf { x }$ can be parameterized by projecting a vector $\mathbf { v }$ to the tangent space. To achieve that, we need to multiply $\mathbf { v }$ with the projection matrix $\bar { \mathbf { P } _ { G _ { \theta } } } ( \mathbf { x } ) = \mathbf { I } - \mathbf { n } _ { G _ { \theta } } ( \mathbf { x } ) \mathbf { \bar { n } } _ { G _ { \theta } } ( \mathbf { \bar { x } } ) ^ { T }$ , where $\mathbf { n } _ { G _ { \theta } } ( \mathbf { x } )$ is the surface normal of point $\mathbf { x }$ . $\mathbf { \bar { P } } _ { G _ { \theta } } ( \mathbf { x } ) \mathbf { v }$ is a tangent vector in the tangent plane of $\mathbf { x }$ . + +Now we are ready to compute the change of tangent dot-product. Let $\mathbf { t } _ { i }$ and $\mathbf { t } _ { j }$ be two arbitrary tangent vectors near point $\mathbf { x }$ at the deformed shape. Further assume that these vectors can be parameterized as $\mathbf { t } _ { i } = \mathbf { P } _ { G _ { \theta } } ( \mathbf { x } ) \mathbf { v } _ { 1 }$ and $\mathbf { t } _ { j } = \mathbf { P } _ { G _ { \theta } } ( \mathbf { x } ) \mathbf { v } _ { 2 }$ . These tangent vector will be transformed by $D _ { \theta }$ into $\mathbf { t } _ { i } ^ { \prime } = \mathbf { J } _ { D _ { \theta } } ( \mathbf { x } ) \mathbf { t } _ { i }$ and $\mathbf { t } _ { j } ^ { \prime } = \mathbf { J } _ { D _ { \theta } } ( \mathbf { \bar { x } } ) \mathbf { t } _ { j }$ . These are tangent vectors at point $\mathbf { y }$ at the input shape. The change of tangent dot-product with respect to these two vectors can be computed as follows: + +$$ +\begin{array} { r } { \vert \mathbf { t } _ { 1 } ^ { T } \mathbf { t } _ { 2 } - \mathbf { t } _ { 1 } ^ { \prime T } \mathbf { t } _ { 2 } ^ { \prime } \vert = \vert \mathbf { v } _ { 1 } ^ { T } \mathbf { P } _ { G _ { \theta } } ( \mathbf { x } ) ^ { T } \left( \mathbf { I } - \mathbf { J } _ { D _ { \theta } } ( \mathbf { x } ) ^ { T } \mathbf { J } _ { D _ { \theta } } ( \mathbf { x } ) \right) \mathbf { P } _ { G _ { \theta } } ( \mathbf { x } ) \mathbf { v } _ { 2 } \vert . } \end{array} +$$ + +To minimize the stretch, we need to enforce that dot-product stays the same for all tangent vectors. This can be done by minimize the matrix norm of $\mathbf { \dot { P } } _ { G _ { \theta } } ^ { T } \bigl ( \mathbf { I } - \mathbf { \dot { J } } _ { D _ { \theta } } ^ { T } \mathbf { J } _ { D _ { \theta } } \bigr ) \mathbf { P } _ { G _ { \theta } }$ . Here, we drop the function arguments $\mathbf { x }$ for the matrix for notation clarity. With these, we define the the stretch loss as: + +$$ +\mathcal { L } _ { s } ( G _ { \theta } ) = \int _ { \mathbf { x } \in \mathcal { M } _ { G _ { \theta } } } \left. \mathbf { P } _ { G _ { \theta } } ^ { T } \left( \mathbf { I } - \mathbf { J } _ { D _ { \theta } } ^ { T } \mathbf { J } _ { D _ { \theta } } \right) \mathbf { P } _ { G _ { \theta } } \right. _ { F } ^ { 2 } d \mathbf { x } . +$$ + +# 5.3.2 Bending Loss + +Bending can be characterized by the change of surface curvature (e.g., making the surface more or less curved). Intuitively, curvature can be described as the change of tangent dot product along the surface normal direction [16, 59]. Let $\mathbf { t } _ { 1 } = \mathbf { P } _ { G _ { \theta } } ( \mathbf { x } ) \mathbf { v } _ { 1 }$ and $\mathbf { t } _ { 2 } = \mathbf { \bar { P } } _ { G _ { \theta } } ( \mathbf { x } ) \mathbf { \bar { v } } _ { 2 }$ be two tangent vectors at $\mathbf { x }$ . Consider the tangent dot product of the surface family $\mathbf { x } + t \mathbf { n } ( \mathbf { x } )$ . Note that this set of surface corresponding to the level sets ${ \bf \dot { \{ p \vert } } G _ { \theta } ( { \bf p } ) = t \}$ if $G _ { \theta }$ is approximating an SDF [54]. Then the change of dot product along the surface normal direction can be given by Hessian and directional derivative: $\begin{array} { r } { \frac { d } { d t } \mathbf { t } _ { 1 } ^ { T } \mathbf { t } _ { 2 } \mathbf { \bar { \Psi } } _ { t = 0 } = \mathbf { t } _ { 1 } ^ { T } \bar { H _ { G _ { \theta } } } ( \mathbf { x } ) \mathbf { t } _ { 2 } } \end{array}$ . Intuitively, the larger this value is, the faster the surface changes whenmal direction, which means the surface has larger curvature. + +Measuring bending amounts to measure the change of tangent dot-product derivative along the surface normal direction. Similar to the previous section, assume we have tangent vectors $\mathbf { t } _ { i } = \mathbf { P } _ { G _ { \theta } } ( \mathbf { x } ) \mathbf { v } _ { i }$ and $\mathbf { t } _ { j } = \mathbf { P } _ { G _ { \theta } } ( \mathbf { x } ) \mathbf { v } _ { j }$ . These tangent vectors are are transformed by the Jacobian of the deformation field $\mathbf { J } _ { D _ { \theta } } ( \mathbf { x } )$ to $\dot { \mathbf { t } } _ { i } ^ { \prime } = \mathbf { J } _ { D _ { \theta } } ( \mathbf { x } ) \mathbf { t } _ { i }$ and $\mathbf { t } _ { j } ^ { \prime } = \mathbf { J } _ { D _ { \theta } } ( \mathbf { x } ) \mathbf { t } _ { j }$ . Since $\mathbf { t } _ { i } ^ { \prime }$ and $\mathbf { t } _ { j } ^ { \prime }$ are tangent vectors at point $\mathbf { y }$ on the surface $\mathcal { M } _ { F }$ , the derivative of tangent dot-product is given by the hessian matrix of field $F$ $: \mathbf { \Gamma } _ { d t } ^ { d } \mathbf { t } _ { 1 } ^ { \prime T } \mathbf { t } _ { 2 } ^ { \prime } | _ { t = 0 } = \mathbf { t } _ { 1 } ^ { \prime T } H _ { F } ( D _ { \theta } ( \mathbf { x } ) ) \mathbf { t } _ { 2 } ^ { \prime } = \mathbf { t } _ { 1 } ^ { T } \mathbf { J } _ { D _ { \theta } } ^ { T } ( \mathbf { x } ) H _ { F } ( D _ { \theta } ( \mathbf { x } ) ) \mathbf { J } _ { D _ { \theta } } ( \mathbf { x } ) \mathbf { t } _ { 2 } .$ . We will drop the function argument to $\mathbf { J } _ { D _ { \theta } }$ , $H _ { G _ { \theta } }$ , and $\mathbf { P } _ { G _ { \theta } }$ for notation clarity. The change of tangent dot-product derivative is: + +$$ +\left| \frac { d } { d t } \left( \mathbf { t } _ { 1 } ^ { T } \mathbf { t } _ { 2 } - \mathbf { t } _ { 1 } ^ { \prime T } \mathbf { t } _ { 2 } ^ { \prime } \right) _ { t = 0 } \right| = \left| \mathbf { v } _ { 1 } ^ { T } \mathbf { P } _ { G _ { \theta } } ^ { T } \left( H _ { G _ { \theta } } - \mathbf { J } _ { D _ { \theta } } ^ { T } H _ { F } ( D _ { \theta } ( \mathbf { x } ) ) \mathbf { J } _ { D _ { \theta } } \right) \mathbf { P } _ { G _ { \theta } } \mathbf { v } _ { 2 } \right| . +$$ + +If there is almost no bending happened between the infinitesimal patches around $\mathbf { x }$ and $\mathbf { y }$ , then the quantity $\begin{array} { r } { \left| \frac { d } { d t } \left( \mathbf { t } _ { 1 } ^ { T } \mathbf { t } _ { 2 } - \mathbf { t } _ { 1 } ^ { \prime T } \bar { \mathbf { t } } _ { 2 } ^ { \prime } \right) _ { t = 0 } \right| } \end{array} \qquad = 0 .$ should stay close to 0 for all pairs of tangent vectors. We will + +quantify this by the matrix norm of ${ \bf P } _ { G _ { \theta } } ^ { T } \left( H _ { G _ { \theta } } - { \bf J } _ { D _ { \theta } } ^ { T } H _ { F } ( D _ { \theta } ( { \bf x } ) ) { \bf J } _ { D _ { \theta } } \right) { \bf P } _ { G _ { \theta } }$ . Finally, we arrive at our bending loss, which minimizes the norm of the matrix that modulate the change of tangent dot-product derivatives moving along the surface normal direction: + +$$ +\mathcal { L } _ { b } ( G _ { \theta } ) = \int _ { x \in \mathcal { M } _ { G _ { \theta } } } \left\| \mathbf { P } _ { G _ { \theta } } ^ { T } \left( H _ { G _ { \theta } } - \mathbf { J } _ { D _ { \theta } } ^ { T } H _ { F } ( D _ { \theta } ( \mathbf { x } ) ) \mathbf { J } _ { D _ { \theta } } \right) \mathbf { P } _ { G _ { \theta } } \right\| _ { F } ^ { s } d \mathbf { x } . +$$ + +# 5.3.3 Computing $\mathcal { L } _ { s }$ and $\mathcal { L } _ { b }$ + +Computing $\mathcal { L } _ { s }$ and $\mathcal { L } _ { b }$ during training requires approximating a surface integral of the form $\begin{array} { r } { \int _ { \mathbf { x } \in \mathcal { M } _ { G _ { \theta } } } \bar { \mathcal { L } } ( \mathbf { x } ) d \mathbf { x } } \end{array}$ using Monte Carlo integration, which requires an efficient way to sample points θuniformly from surface $\mathcal { M } _ { G _ { \theta } }$ . While it is feasible to sample uniformly from an SDF, this is challenging to do with $G _ { \theta }$ since there is no guarantee that $G _ { \theta }$ remains a valid SDF during the course of training. Thanks to the invertibility of $D _ { \theta }$ , we can apply change of variable $\mathbf { x } = D _ { \theta } ^ { - 1 } ( \mathbf { y } )$ to the integration, where $\mathbf { y }$ are points on the input surface $\mathcal { M } _ { F }$ : + +$$ +\int _ { \mathbf { x } \in \mathcal { M } _ { G _ { \theta } } } \mathcal { L } ( \mathbf { x } ) d \mathbf { x } = \int _ { \mathbf { y } \in \mathcal { M } _ { F } } \mathcal { L } ( \mathbf { x } ) \left| \operatorname* { d e t } \left( \mathbf { J } _ { D _ { \theta } } ( \mathbf { x } ) \mathbf { P } _ { G _ { \theta } } ( \mathbf { x } ) + \mathbf { n } _ { F } ( \mathbf { y } ) \mathbf { n } _ { G _ { \theta } } ( \mathbf { x } ) ^ { T } \right) \right| ^ { - 2 } d \mathbf { y } . +$$ + +$\mathbf { J } _ { D _ { \theta } } \mathbf { P } _ { G _ { \theta } } \in \mathbb { R } ^ { 3 \times 3 }$ maps tangent vector from $\mathcal { M } _ { G _ { \theta } }$ to $\mathcal { M } _ { F }$ . We apply the extension trick from Iglesias et al. [35] to create a matrix whose determinant equals the change of surface area. This is achieved by adding the surface normal component $\mathbf { n } _ { F } \mathbf { n } _ { G } ^ { T }$ and keeping it unchanged. With this change of variable, we now can compute the losses with point samples from the input field $F$ . Since the input field $F$ approximates an SDF, we can use the method introduced in Section 5.1 to sample uniform points. + +# 5.4 Optimization + +Putting the losses together, we deform a neural field by solving the constrained optimization problem + +$$ +\underset { \theta } { \arg \operatorname* { m i n } } \lambda _ { s } \mathcal { L } _ { s } ( G _ { \theta } ) + \lambda _ { b } \mathcal { L } _ { b } ( G _ { \theta } ) , \quad \mathrm { s . t . } \forall 1 \leq i \leq n , \ \| D _ { \theta } ( \mathbf { t } _ { i } ) - \mathbf { h } _ { i } \| = 0 +$$ + +where $\lambda _ { s } , \lambda _ { b }$ are hyperparameters that determine the material properties. One way to solve this constrained optimization problem for a neural network is to make the constraints a soft loss adding to the objective function: $\begin{array} { r } { \dot { \mathcal { L } } _ { c o n s t } ^ { { \bf \Delta } } ( D _ { \theta } ) = \frac { 1 } { n } \sum _ { 1 = 1 } ^ { n } \left. D _ { \theta } ( \mathbf { t } _ { i } ) - \mathbf { h } _ { i } \right. } \end{array}$ . Our final objective is: + +We set $\lambda _ { c }$ to be a high value to enforce that the model satisfies user-specified input as much as possible. The user can tune $\lambda _ { b }$ and $\lambda _ { s }$ depending on the application scenario. We optimize $\mathcal { L } ( \boldsymbol { \theta } )$ with Adam optimizer to obtain the output field $G _ { \theta }$ . Hyperparameters are provided in the supplement. + +# 6 Deformation Results + +In this section, we will demonstrate the results of our methods to shape deformation. The shapes for deformation are taken from Sorkine-Hornung and Alexa [70]. To create neural fields from these meshes, we follow the procedure of Park et al. [56] to compute ground-truth SDF for locations sampled within $[ - 1 , 1 ] ^ { 3 }$ . We then fit a SIREN [66] to the ground-truth SDF to generate our initial neural fields. Our main baseline is ARAP [70, 86]. The simplest way to use ARAP to edit neural fields is applying it on a mesh extracted from the input neural fields using marching cubes [44, 45]. We first present results comparing with ARAP applied to the extracted mesh. Then we will conduct an analysis to show our losses encourage the right behaviors. + +Comparing to ARAP baseline. We follow ARAP [70] to create a set of basic shape deformation operations to evaluate our algorithm. In this setting, the user will first specify a set of handles used for manipulation (shown in Figure 5 in blue). In general, the user can apply three basic types of operation on a handle: 1) make it static (i.e., no deformation), 2) translate it, or 3) rotate it around a center. Usually, the first operation is used in combination with the latter two to produce useful deformation. We first show how our algorithm deforms simple objects (e.g., a cylinder and a rectangle bar) when the user rotates or translates one end while fixing the other. We then extend this set of operations to shapes with more detail (e.g., Cactus, Armadillo, and Dino). Finally, we test our algorithms when all three operations are specified together on a single shape. The results are shown in Figure 5. We can see that applying ARAP directly on the extracted mesh creates undesirable volume distortion. Our algorithm is able to produce deformation results that are natural while satisfying the user’s intention. + +![](images/4b0800ba8a5e03bd4ddc57775de98cce018d0745cceb87a6a5d10c6b16f46363.jpg) +Figure 5: Deformation results. (A) Input shape. (B) Baseline. (C) Ours. Red points are user specified handles $\mathbf { h } _ { i }$ . Blue points denote user specified target points $\mathbf { t } _ { i }$ . First row: single rotation or translation on simple shapes. Second and third rows: single rotation or translation on more complex objects. Fourth row: multiple edits on complex objects. + +Comparing to different ARAP variants. This artifact is partially due to the surface discretization made by the marching cubed algorithm doesn’t agree with the assumptions made by ARAP [41]. To verify this hypothesis, we also include three additional baselines in Figure 6. First, we show the results of applying ARAP on the low-poly mesh used to create the input neural fields (Original). Second, we first apply Garland and Heckbert [28] to simplify the surface of the extracted mesh before applying ARAP to it (Remeshed). Finally, we also compare to the results of SR-ARAP [41], which adds smoothness regularization to ARAP to remove some unnatural distortion (SR-ARAP). The figure shows that ARAP works much better when the surface is discretized appropriately. Discretizing the surface, however, usually requires case-by-case manual adjustment to perform well. Our algorithm does not suffer from such issues as we optimize the thin shell objective directly without committing to a particular discretization of the surface. + +Loss analysis. Here we provide an experiment to analyze the behavior of stretching loss and bending loss. Specifically, we compare models optimized for only the stretching loss $\mathcal { L } _ { s }$ , only the bending loss $\mathcal { L } _ { b }$ , and both losses together. Similar to Section 5.2, we deform a neural field that approximates the SDF of a 2D rectangle. The results are shown in Figure 7. Optimizing only for $\mathcal { L } _ { s }$ produces a shape that best preserves surface area (or the perimeter in the 2D case), which explains the wiggling. Optimizing only for $\mathcal { L } _ { b }$ produces a shape that tries to prevent wiggling of the surface, which changes the curvature of the surface. The user can choose appropriate $\lambda _ { s }$ and $\lambda _ { b }$ to produce deformation with resistance to both bending and stretching. + +![](images/2de287fec84c55f2a62835e84347ec2e58c183b03740c6cd0bb69c78658d3bc9.jpg) +Figure 6: Additional ARAP baselines. Directly applying ARAP to extracted mesh produces poor results (i.e., MC). While this can be alleviated by remshing (i.e. Original or Remeshed) or regularization (i.e. SR-ARAP), this shows mesh deformation algorithms can be sensitive to discretization quality. Our method do not discretize the surface, thus circumvent such issue. Red points are handles; Blue points are targets. + +# 7 Discussion, Limitations, and Future work + +Advantages of using neural fields for geometry processing. The main strength of using neural fields for geometry processing is that one can disentangle the processing algorithm from the surface discretization. Users do not need to worry about discretization while manipulating a shape represented in neural fields. This might open the door to more automatic geometry processing pipelines. Additionally, neural fields are modular and can be combined with other neural networks. Neural fields can be easily incorporated into current deep learning pipelines. This makes them well-suited for data-driven applications. + +![](images/019673aff3153b24234a310391ed42d9c81088591fddf2cc7eb418d921800332.jpg) +Figure 7: Analysis of stretching and bending losses. Blue points are handles; Red points are targets. + +Limitations and future directions. The main limitation of our method is the slow optimization speed that hinders interactive editing. Typically, ARAP can solve each of such deformation problems within half an hour for large meshes, and it can achieve interactive speed for meshes with a small number of triangles. The Taubin smoothing can finish in a couple of seconds. Our deformation method right now requires a TitanX GPU with 12GB memory to train for 10 hours. Our smoothing and sharpening method takes about 10 minutes on the same GPU. The current algorithm does not ensure that the output field remains an SDF, which prevents performing multiple editing operations. + +We believe many of these limitations can be addressed in future work. One can potentially use techniques like progressive training or meta-learning [67, 75] to improve the training speed. To allow consecutive editing, we can design regularization loss that enforces the output fields to approximate an SDF [4] or design sampling methods robust with noisy SDF. Other interesting directions include providing deeper theoretical analysis and applying neural fields in other geometry processing tasks. + +Societal impact. Our work can lead to more efficient geometry processing algorithms. Such algorithms can empower artists to generate creative content. Potential negative impact includes misuse of geometry processing algorithms to create offensive content. + +# 8 Conclusion + +Our work provides a proof of concept that geometry processing can be done entirely with neural fields without discretizing the surface. We develop network architectures and training objectives for filtering and deforming shapes represented by neural fields and demonstrate the advantages of using neural fields for geometry processing. We hope that our work can inspire a new generation of geometry processing algorithms using neural fields. + +Acknowledgement. Guandao’s PhD was supported in part by a research gift from Magic Leap and a donation from NVIDIA. We want to thank Wenqi Xian, Professor Steve Marschner, and members of Intel Labs for providing insightful feedback for this project. + +References [1] M. Alexa, D. Cohen-Or, and D. Levin. As-rigid-as-possible shape interpolation. 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Open3D: A modern library for 3D data processing. arXiv:1801.09847, 2018. 8 \ No newline at end of file diff --git a/parse/train/JG-SlCAx5_K/JG-SlCAx5_K_content_list.json b/parse/train/JG-SlCAx5_K/JG-SlCAx5_K_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..3b6495eee440c2d69ed0293e50a7c9f46be87670 --- /dev/null +++ b/parse/train/JG-SlCAx5_K/JG-SlCAx5_K_content_list.json @@ -0,0 +1,1412 @@ +[ + { + "type": "text", + "text": "Geometry Processing with Neural Fields ", + "text_level": 1, + "bbox": [ + 253, + 122, + 745, + 147 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Guandao Yang ∗ Cornell University ", + "bbox": [ + 192, + 202, + 315, + 229 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Serge Belongie University of Copenhagen ", + "bbox": [ + 338, + 202, + 509, + 229 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Bharath Hariharan Cornell University ", + "bbox": [ + 535, + 202, + 673, + 228 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vladlen Koltun Intel Labs ", + "bbox": [ + 696, + 202, + 807, + 228 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract ", + "text_level": 1, + "bbox": [ + 462, + 265, + 535, + 281 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most existing geometry processing algorithms use meshes as the default shape representation. Manipulating meshes, however, requires one to maintain high quality in the surface discretization. For example, changing the topology of a mesh usually requires additional procedures such as remeshing. This paper instead proposes the use of neural fields for geometry processing. Neural fields can compactly store complicated shapes without spatial discretization. Moreover, neural fields are infinitely differentiable, which allows them to be optimized for objectives that involve higher-order derivatives. This raises the question: can geometry processing be done entirely using neural fields? We introduce loss functions and architectures to show that some of the most challenging geometry processing tasks, such as deformation and filtering, can be done with neural fields. Experimental results show that our methods are on par with the well-established mesh-based methods without committing to a particular surface discretization. Code is available at https://github.com/stevenygd/NFGP. ", + "bbox": [ + 233, + 299, + 766, + 492 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Introduction ", + "text_level": 1, + "bbox": [ + 174, + 523, + 310, + 540 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In many graphics applications, users may want to edit digital shapes using just a few clicks, such as making a character bow by dragging the head downwards. Such manipulation from sparse input requires geometry processing algorithms. Most of these algorithms use polygonal meshes to represent shapes [11]. Polygonal meshes were created initially for researchers as a representation of real-world shapes that they can both interpret and manipulate [14, 52, 78]. However, developing algorithms that automatically manipulate meshes is often difficult since they involve discretizing the surface. For example, changing the topology of a mesh, such as turning a sphere into a torus, will break such discretization and require additional repair procedures such as remeshing [2, 3]. Given that shape editing is increasingly performed by algorithms, it seems worthwhile to search for a shape representation that is more amenable to automatic geometry processing. ", + "bbox": [ + 174, + 558, + 825, + 695 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "An alternative to the polygonal mesh is an implicit representation, in which the surface is represented by a level set of a field: $\\bar { \\{ x \\vert f ( x ) = c \\} }$ [22, 39, 63]. Since it is easy to change shape topology using implicit representations, people have applied them for geometry processing tasks such as shape merging [8, 51, 54]. These works store implicit fields using voxels or octrees, which introduce memory-intensive spatial discretization. Recent research addresses this by using continuous neural networks to represent implicit fields [19, 45, 46, 56]. These neural fields possess several advantages in addition to the merits inherited from implicit representation: they are compact to store [23, 45] and can produce high-quality continuous surfaces at arbitrary resolutions [45, 56]. The community has achieved compelling results using neural fields in a variety of applications [47, 64, 73, 84]. Notwithstanding these results, it is still unclear whether shape editing tasks challenging for implicit fields (e.g., deformation and filtering) can be performed with neural fields. In this paper, we ask: can geometry processing be done entirely using neural fields? ", + "bbox": [ + 174, + 702, + 825, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Geometry processing tasks are challenging because they are typically under-constrained: user input is very sparse. Therefore, we need to leverage priors that characterize how a natural surface behaves. Such surface priors are usually instantiated by minimizing energy functionals that describe the physical properties of surfaces using operators from differential geometry. For example, one can encourage surfaces to be smooth by minimizing the curvature, which can be measured by the LaplaceBeltrami operator. Such operators, however, require a parameterization of the surface, which is not available for level sets of a neural field. Mesh algorithms usually approximate these geometric operators using the geodesic neighbors of the surface point. This allows the algorithms to focus on intrinsic geometric properties that are independent of shape parameterization. However, it is not easy to obtain geodesic neighbors in a neural field since the surface of interest is encoded implicitly by a set of points that evaluate the field function to the same value. ", + "bbox": [ + 174, + 90, + 825, + 243 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We posit that computing these geometric operators in neural fields requires a fundamentally different approach. The idea is to approximate the local surface of the level set using the derivatives of the underlying field. We can evaluate intrinsic geometry properties of the level set, such as curvature, using only the field derivatives [39, 54]. This allows us to develop loss functions that describe surface priors such as elasticity or rigidity. To achieve this, we use the fact that neural fields are designed to be infinitely differentiable [66, 74]. The infinite differentiability of neural fields makes it possible to optimize loss functions that involve higher-order derivatives using gradient descent methods. Thus, unlike mesh-based geometry processing algorithms that approximate these objectives using surface discretizations, we can directly optimize in terms of the derivatives of the field. ", + "bbox": [ + 174, + 250, + 825, + 375 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our formulation provides a proof of concept that geometry processing can be done entirely using neural fields. In particular, we focus on two tasks: shape filtering (e.g., smoothing and sharpening) and topology-preserving deformations. These two tasks are not only essential for downstream applications but also bring out the known challenges associated with implicit representations. We first tackle shape sharpening and smoothing and show how these can be done by optimizing a loss function based on geometric properties computed via the neural field’s derivatives. To achieve shape deformation, we propose to warp the neural field using a deformation vector field modeled by an invertible neural network [7]. With this invertible deformation field, we derive a training objective that models the implicitly represented surfaces as elastic shells. ", + "bbox": [ + 174, + 381, + 825, + 506 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We compare our method with well-established mesh-based baselines [70, 76]. Our method can match the quality of the mesh-based counterparts without discretizing the surface. We hope that our work can inspire future generations of geometry processing algorithms using neural fields. ", + "bbox": [ + 176, + 511, + 825, + 554 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 Related Work ", + "text_level": 1, + "bbox": [ + 174, + 571, + 321, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper builds on two bodies of work: polygon mesh geometry processing and neural field representations. We will focus on prior work on two geometry processing tasks: shape filtering and topology-preserving deformation. Please refer to Botsch et al. [11] for further reading. ", + "bbox": [ + 176, + 603, + 823, + 645 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Mesh smoothing (and sharpening). The goal of mesh smoothing is to remove high-frequency noise and produce a smooth surface. Noise removal can be achieved by Fourier analysis [76, 79] or by modeling surface motion with a diffusion equation [26]. Smoothness can be promoted by minimizing energy functionals inspired by differential operators [50, 72, 82]. Sharpening is the inverse of smoothing. In this paper, we adopt the goal of smoothing from prior work [20, 76] and design a corresponding differentiable objective for neural fields. ", + "bbox": [ + 174, + 660, + 823, + 742 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Implicit field smoothing. Implicit representations can be smoothed by evolving the level set according to its curvature normal [49, 54]. Many network architectures, such as ReLU MLP, bias toward smoothness when modeling an implicit field [61, 66, 74]. Regularization objectives and initialization schemes have been proposed to obtain smooth level sets from scanned surface points [5, 31]. These works mostly use smoothness as a prior when training neural fields. Our work formulates an objective that allows smoothing or sharpening a neural field as desired. ", + "bbox": [ + 174, + 757, + 825, + 840 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Mesh deformation. Mesh deformation is done by either deforming the shape (i.e. vertices) [9, 69] or the space [6, 36, 41, 48, 65]. These algorithms usually draw inspiration from physics and differential geometry to develop energy functions that encourage natural deformation [10, 15, 24, 70, 71, 77]. They also linearize such objectives so that they can be solved efficiently using linear solvers [9]. Recent research also applies deep learning to optimize for non-linear deformation losses [32, 34, 38, 80, 81, 83]. Deforming a mesh, however, requires estimating the deformation objectives with spatial discretization and maintaining vertex connectivity in a way that preserves topology [42]. We deform neural fields with a continuous invertible field to circumvent these issues. ", + "bbox": [ + 176, + 856, + 823, + 911 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 92, + 825, + 147 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Implicit field deformation. Prior works have studied the deformation of implicit fields for tasks like physics simulation [39, 51, 54, 55]. These works use voxels or octrees to represent implicit fields, while our paper advocates for using neural fields for deformation. There is some past work on deforming neural fields to match a target shape [12, 18, 37, 53, 58] or image [43, 57, 60] without any correspondences between the two. In contrast, we perform such deformation with very few localized user-provided correspondences, but without any other information about the target shape. Our setting is very convenient for artists, but it requires the algorithm to provide a strong surface prior due to the lack of a densely specified target state. Other prior works on editing neural fields are trained on a dataset of shapes from a particular object category [25, 29, 30, 33, 85]. Since surface priors are specified implicitly by the dataset, it is unclear how to apply these methods to out-of-distribution shapes. In contrast, our paper requires no training dataset and instead enforces priors inspired by more general physical properties such as smoothness and elasticity. Remelli et al. [62] developed a way to differentiate iso-surface extraction, which allows deforming neural fields using objectives carried over from mesh-based algorithms. Our method avoids iso-surface extraction entirely and formulates differentiable deformation objectives directly on the implicit field. ", + "bbox": [ + 173, + 162, + 825, + 371 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 Computing Surface Properties of Neural Fields ", + "text_level": 1, + "bbox": [ + 174, + 391, + 599, + 409 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we will discuss how to compute surface properties using neural fields and establish notation for the following sections. Let $\\partial \\Omega$ be a surface enclosing the region $\\Omega$ . A signed distance field (SDF) for surface $\\partial \\Omega$ is defined as $d ( \\mathbf { x } ) = s ( \\mathbf { x } ) \\operatorname* { m i n } _ { \\mathbf { y } \\in \\partial \\Omega } \\bar { \\| } \\mathbf { x } - \\mathbf { y } \\bar { \\| }$ . The sign function $s ( \\mathbf { x } )$ evaluates to $- 1$ if $\\textbf { x } \\in { \\Omega }$ and 1 otherwise. We will assume that a neural field approximate an SDF whose zero-isosurface represents the surface of interest. For a neural field $f$ , we denote its zero-isosurface using $\\mathcal { M } _ { f }$ . This section summarizes how to compute surface normals and curvatures from neural fields. This is well-understood and we summarize this here for convenience [39, 54, 59]. ", + "bbox": [ + 174, + 422, + 825, + 521 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Surface normal. The surface normal is the vector perpendicular to the tangent plane and describes the local orientation of the surface. For an SDF, the outward oriented surface normal of its level set is the field gradient: $\\mathbf { n } _ { d } ( \\mathbf { x } ) = \\nabla _ { \\mathbf { x } } d ( \\mathbf { x } )$ . It can be shown that the SDF’s gradient norm is always one: $\\lVert \\nabla _ { \\mathbf { x } } d ( \\mathbf { x } ) \\rVert = 1$ . This property can be used to ensure that the field remains a valid SDF throughout any manipulation [4, 31]. The closest point in $\\partial \\Omega$ from $\\mathbf { x }$ can be found by $\\mathbf { x } - d ( \\mathbf { x } ) \\mathbf { n } _ { d } ( \\mathbf { x } )$ . This property can be used to sample points from the isosurface without creating a mesh [5, 13]. Finally, since the tangent plane is perpendicular to the surface normal, we can project vectors onto the tangent plane by subtracting their projection onto the normal using the following projection matrix $\\mathbf { x }$ : $\\mathbf { P } _ { d } \\mathbf { \\bar { ( x ) } } \\overset { \\mathbf { \\bar { \\alpha } } } { = } \\mathbf { I } - \\mathbf { \\bar { n _ { d } } } \\mathbf { ( x ) } \\mathbf { n } _ { d } \\mathbf { ( x ) } \\mathbf { \\breve { \\alpha } }$ . This projection matrix allows us to characterize the tangent plane. This matrix is important for measuring how much a given deformation stretches the tangent direction [35]. ", + "bbox": [ + 174, + 536, + 825, + 676 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Curvature. Intuitively, curvature describes how much a surface deviates from a plane. This can be captured by the total derivative of the surface normal, which is also known as the shape operator: $\\bar { \\mathbf { \\xi } } S _ { D } ( \\bar { \\mathbf { x } } ) = \\mathcal { D } \\bar { \\mathbf { n } _ { d } } ( \\mathbf { x } )$ . For an SDF, the normal itself is given by the derivative of the field, thus the shape operator for an SDF is the Hessian of the field function: $\\dot { H _ { d } } ( \\mathbf { x } ) = \\mathcal { D } ^ { 2 } d ( \\mathbf { x } )$ . The shape operator can be used to capture many different notions of curvature, including mean curvature (half the trace of $S _ { D } ( \\mathbf { x } )$ , denoted by $\\bar { \\kappa }$ ), Gaussian curvature (the determinant of $S _ { D } ( { \\bf x } ) _ { , }$ ), and principal curvatures (the eigenvalues of $S _ { D } ( { \\bf x } ) _ { , }$ ). We will use these to define objectives that smooth or sharpen the surface. ", + "bbox": [ + 174, + 691, + 825, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4 Shape Smoothing and Sharpening ", + "text_level": 1, + "bbox": [ + 174, + 809, + 490, + 827 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we will show that shape smoothing and sharpening can be done directly on neural fields without producing meshes. In our setup, the input shape is represented as the zero-isosurface $\\mathcal { M } _ { F }$ of the neural field $F$ . The algorithm needs to output neural field $G _ { \\theta }$ whose zero-isosurface $\\mathcal { M } _ { G _ { \\theta } }$ satisfies two goals. First, $\\mathcal { M } _ { G _ { \\theta } }$ should preserve the global structure of $\\mathcal { M } _ { F }$ . Second, the surface $\\mathcal { M } _ { G _ { \\theta } }$ should make desired changes to match the curvature of shape $\\mathcal { M } _ { F }$ . ", + "bbox": [ + 174, + 842, + 825, + 911 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a582fb6a973a707da2ca642467983ef490d9b46ef69834159125364e1493a4b2.jpg", + "image_caption": [ + "Figure 2: Smoothing and sharpening results. (A) zoomed-in input; (B) our method; (C) baseline without remeshing; (D) baseline with remeshing. We can see that the baseline without remeshing finds it difficult to smooth or sharpen the mesh extracted from neural fields. Our method is able to achieve good results without discretizing the surface. " + ], + "image_footnote": [], + "bbox": [ + 178, + 88, + 823, + 290 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve these goals, we first instantiate $G _ { \\theta }$ using the same architecture and parameter values as $F$ Then we optimize $G _ { \\theta }$ using the following objective: ", + "bbox": [ + 173, + 367, + 825, + 396 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/318f4b7b85ff34c65448f1858758db87fc47d86433ef6e6cdd2a92d8816934ea.jpg", + "text": "$$\n\\mathcal { L } ( \\theta ) = \\int _ { \\mathbf { x } \\in U } \\left| G _ { \\theta } ( \\mathbf { x } ) - F ( \\mathbf { x } ) \\right| ^ { 2 } + \\lambda _ { g } \\left( \\left\\| \\nabla _ { \\mathbf { x } } G _ { \\theta } ( \\mathbf { x } ) \\right\\| - 1 \\right) ^ { 2 } d \\mathbf { x } + \\int _ { \\mathbf { x } \\in V _ { \\tau } } \\lambda _ { k } \\left( \\kappa _ { G _ { \\theta } } ( \\mathbf { x } ) - \\beta \\kappa _ { F } ( \\mathbf { x } ) \\right) ^ { 2 } d \\mathbf { x } .\n$$", + "text_format": "latex", + "bbox": [ + 179, + 406, + 813, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The first integral encourages the network $G _ { \\theta }$ to preserve the original shape. The second term regularizes $G _ { \\theta }$ to remain a valid SDF by enforcing that the norm of the gradient is 1 (i.e., the Eikonal constraint [4, 31]). The integration is over the region $U$ where the original neural field $F$ is supervised over. The final term aims to smooth or sharpen the surface by increasing or decreasing the curvature $\\kappa$ . Setting $\\beta < 1$ will decrease the curvature of the output surface $\\kappa _ { G _ { \\theta } }$ , resulting in a smoother shape. $\\beta > 1$ will lead to surfaces with higher curvature details and will thus sharpen shapes. In this paper, we will use mean curvature since it’s easy to compute with neural fields: $\\kappa _ { f } ( \\mathbf { x } ) = \\mathrm { t r } \\mathcal { D } ( \\mathbf { n } _ { f } ( \\mathbf { x } ) )$ . ", + "bbox": [ + 174, + 483, + 614, + 636 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f46db6fa8fd3ad41d2bd57bfbf0b5032fd160bdb630f47e8f74bab8da49662dd.jpg", + "image_caption": [ + "Figure 1: L: SIREN learned to fit the SDF of a square; R: Zooming in on the surface. " + ], + "image_footnote": [], + "bbox": [ + 627, + 487, + 821, + 582 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "One challenge is that the computation of curvature can be very noisy for neural fields using periodic activations. Figure 4 shows how an ostensibly smooth isosurface learned through SIREN [66] is actually quite rough when zoomed in. The curvature evaluated on such a rough surface can be too noisy to be used for training. To alleviate this issue, we only compute the curvature regularization in areas where the curvature of the level set is less than a certain threshold $\\tau$ . Formally, we define this area as $V _ { \\tau } = \\{ \\mathbf { x } \\in U | \\operatorname* { m a x } ( | \\kappa _ { G _ { \\theta } } | , | \\kappa _ { F } | ) < \\tau \\}$ . We use rejection sampling to sample points from $V _ { \\tau }$ when computing the loss during training. ", + "bbox": [ + 173, + 642, + 825, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Results. We follow prior works [20, 76] to use Armadillo [40] and a sphere with one half of it corrupted by Gaussian noise. We compare our algorithm to two baselines. The first baseline directly applies the smoothing algorithm developed by Taubin [76] to the mesh extracted from the neural field using Marching cube [44]. The second baseline applies the filtering algorithms on meshes simplified by quadratic decimation [27]. The input neural fields are created following the procedure of Park et al. [56]. The results are shown in Figure 2. The first baseline fails to smooth or sharpen the surface appropriately. It only modifies the surface with high-frequency noise. While the second baseline can filter the surface correctly, it introduces discretization artifacts due to the decimation process. This suggests it is challenging to filter the neural field surface with mesh processing algorithms since these algorithms are sensitive to the quality of surface discretization. On the other hand, our algorithm can produce good filtering results without the need to maintain a good discretization of the surface. ", + "bbox": [ + 173, + 758, + 825, + 911 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5 Deformation ", + "text_level": 1, + "bbox": [ + 173, + 89, + 312, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To deform a shape, the user will choose a set of deformation handles $\\{ { \\bf h } _ { i } \\} _ { i = 1 } ^ { n }$ . For each handles $\\mathbf { h } _ { i }$ , the user will specify a target location $\\mathbf { t } _ { i }$ describing where the handle will be dragged to. Users can set $\\mathbf { t } _ { i } = \\mathbf { h } _ { i }$ to enforce a part of the surface to be unchanged. Given this input, there are two goals for the shape deformation algorithm: 1) satisfying user inputs and 2) ensuring that the deformation resembles the natural behavior of real objects. The input shape will be represented by the zero-isosurface of a neural field $F$ in our setting. The algorithm must therefore output a neural field $G _ { \\theta }$ whose zero-isosurface represents the deformed shape that satisfies the aforementioned two goals. ", + "bbox": [ + 173, + 119, + 826, + 218 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this setting, deformation can be formulated as solving a constrained optimization problem: ", + "bbox": [ + 171, + 223, + 784, + 238 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/d2141fab6172c932163522b1a6abc7db12b2a399d6dea33ec0fdf70bc739ed9e.jpg", + "text": "$$\n\\operatorname* { m i n } _ { \\theta } \\ \\mathcal { L } _ { d f m } ( G _ { \\theta } , F ) \\quad \\mathrm { s . t . } \\ \\mathcal { L } _ { c o n s t } ( G _ { \\theta } , \\mathbf { t } _ { i } , \\mathbf { h } _ { i } ) = 0 , 1 \\leq i \\leq n ,\n$$", + "text_format": "latex", + "bbox": [ + 299, + 244, + 694, + 267 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the objective $\\mathcal { L } _ { d f m } ( G _ { \\theta } , F )$ measures how natural the deformation is. The constraints $\\mathcal { L } _ { c o n s t } ( G _ { \\theta } , \\mathbf { t } _ { i } , \\mathbf { h } _ { i } ) = 0$ ensure that the result deformation matches user input. ", + "bbox": [ + 173, + 275, + 826, + 304 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "One way to ensure a natural-looking deformation is to assume that the surface behaves like a thin elastic shell, which is resistant to stretching and bending [1, 70]. Traditional mesh-based algorithms model elasticity by minimizing the thin shell energy that penalizes stretching or bending happened to any local patch. Naively adapting such training objectives from mesh-based algorithms to neural fields is challenging because these algorithms assume dense correspondences between two surfaces and efficient access to geodesic neighbors. ", + "bbox": [ + 174, + 309, + 825, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we will address these challenges by following strategy. To measure how much bending or stretching happened to the whole surface, we will first divide the surface into infinitesimal patches and then sum the amount of bending or stretching that happened to each patch. To achieve that, we first develop a sampling schema to sample these infinitesimal patches uniformly from the input shapes (Sec 5.1). Then we warp the input shape with an invertible neural network to achieve correspondences between the input and output surfaces (Sec 5.2). Finally, we derive ways that measure the amount of bending and stretching between two infinitesimal surface patches (Sec 5.3). ", + "bbox": [ + 173, + 398, + 825, + 497 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1 Sampling ", + "text_level": 1, + "bbox": [ + 174, + 512, + 279, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our first step is to sample infinitesimal surface patches uniformly to the surface area from the zero-isosurface of the neural field. Each infinitesimal surface patch can be represented by a surface point and its local derivatives. With this said, the problem amounts to sampling points from the zero-isosurface. Formally, we are given a neural field $F$ that approximates the signed distance field of the input shape. The goal is to find a way to sample an arbitrary number of points on its zero-isosurface $\\mathcal { M } _ { F }$ . One way to sample points from $\\mathcal { M } _ { F }$ is to run Langevin dynamics using the gradient of the field $F$ [5, 13]: $\\mathbf { x } _ { t + 1 } \\overset { \\cdot } { = } \\tilde { \\mathbf { x } } _ { t } - F ( \\tilde { \\mathbf { x } } _ { t } ) n _ { F } ( \\tilde { \\mathbf { x } } _ { t } )$ , $\\tilde { \\mathbf { x } } _ { t } \\sim \\mathcal { N } ( \\mathbf { x } _ { t } , \\sigma \\mathbf { I } )$ . $\\mathbf { x } _ { \\mathrm { 0 } }$ are initialized by sampling uniformly within $[ - 1 , 1 ] ^ { 3 }$ . Here we also leverage an SDF property: the closest surface point to $\\mathbf { x }$ can be computed by ${ \\bf x } - { \\bf n } ( { \\bf x } ) F ( { \\bf x } )$ (Sec 3). While this process produces points guaranteed to be on the zero-isosurface, the mixing time of the procedure is very long without appropriate coarse-to-fine annealing [68]. Running this process for limited iterations results in point samples that are concentrating near the high curvature area, as shown on the left side of Figure 5.1. ", + "bbox": [ + 174, + 537, + 550, + 676 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1bb5cd9809445b92975f25d3de02307121f0571a65d61bf8b055406cdc447ce9.jpg", + "image_caption": [ + "Figure 3: Sampling from dino. L: no rejection; R: ours (with rejection). " + ], + "image_footnote": [], + "bbox": [ + 562, + 541, + 823, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 676, + 825, + 761 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To alleviate this issue, we instantiate the sampling procedure with $\\mathbf { x } _ { \\mathrm { 0 } }$ sampled from a rough shape. This can be done by first sampling uniformly from the bounded space and rejecting points that are too far away from the isosurface: $\\mathbf { x } _ { 0 } \\sim \\{ \\mathbf { x } \\in U ( - 1 , 1 ) | F ( \\mathbf { x } ) < \\tau _ { s } \\}$ . We found that $\\tau _ { s }$ can be set to a relatively large number (e.g., about 0.1). This prevents high rejection rates without sacrificing sampling quality. Figure 5.1 shows that our method creates uniform samples. ", + "bbox": [ + 173, + 766, + 825, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We quantitatively evaluate the effectiveness of the sampling scheme. Specifically, we compare our sampling scheme with directly applying Langevin dynamics [13] ( $L D$ in Table 1). To do that, we compute the Chamfer Distance (CD) and Earth Mover Distance (EMD) between points sampled by the valuated algorithms and points sampled uniformly from the extracted mesh. For both metrics, lower values indicate better performance Since larger surfaces can lead to larger CD and EMD values, we normalize the metrics by the values obtained by comparing two sets of uniform samples from the mesh (i.e., CDr and EMDr) The results show that initializing $\\mathbf { x } _ { \\mathrm { 0 } }$ by rejection sampling significantly improves both CD and EMD compared to naively applying Langevin dynamics, at a minor cost in sampling time. ", + "bbox": [ + 174, + 842, + 825, + 911 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 90, + 825, + 147 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2 Invertible Deformation Field ", + "text_level": 1, + "bbox": [ + 174, + 167, + 413, + 183 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After we obtained surface points samples from zero isosurfaces of the input neural fields, the next step is to deform these surface points to the output shapes. One way to deform neural fields is to warp the coordinate space of the input network using a deformation field predicted by a neural network $D _ { \\theta }$ [25, 43, 57]. Under this framework, the output network can be defined as $G _ { \\theta } ( \\mathbf { x } ) = F ( D _ { \\theta } ( \\mathbf { x } ) )$ . Then the constraint $\\mathcal { L } _ { c o n s t } ( G _ { \\theta } , \\mathbf { t } , \\mathbf { h } )$ can be defined as $\\mathcal { L } _ { c o n s t } ( G _ { \\theta } , \\mathbf { t } , \\mathbf { h } ) = \\| D _ { \\theta } ( \\mathbf { t } ) - \\mathbf { h } \\|$ . ", + "bbox": [ + 174, + 195, + 550, + 321 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1e60e5f175445785ae5b7f05d14eca9ff4503fbba92a5039188753eade047450.jpg", + "table_caption": [ + "Table 1: Our sampling method achieves better results than the baseline. " + ], + "table_footnote": [], + "table_body": "
Dino Armadillo
MetricsLDOursLDOurs
CDr (↓)1.541.041.361.02
EMDr (↓)3.381.153.301.08
Time0.150.210.120.18
", + "bbox": [ + 562, + 226, + 828, + 319 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ideally, we would like the deformation $D _ { \\theta }$ to be continuous and invertible. This will allow us to create well-behaved one-to-one correspondences between points on the deform shape (i.e., x) and points on the input shape (i.e., $D _ { \\theta } ( \\mathbf { x } ) )$ . To achieve this, we make $D _ { \\theta }$ to be an invertible network composed of a sequence of invertible residual blocks [7]. ", + "bbox": [ + 174, + 325, + 825, + 382 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Invertible residual block. Prior works [7, 17] have shown that a sufficient condition for the residual block $f ( x ) = x + g ( x )$ to be invertible is that the Lipschitz constant of function $g$ is less than 1. The architecture of the network $g ( x )$ is usually composed of spectral normalized linear layers and Lipschitz continuous nonlinearities such as ELU [21]. The inverse of such residual block can be computed by finding the fixed point of function $y \\mapsto y - g ( x )$ [7]. Intuitively, deforming using one invertible residual block amounts to moving point $x$ with deformation vector $g ( x )$ . ", + "bbox": [ + 173, + 401, + 825, + 486 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Lipschitz continuous positional encoding. Applying such architecture directly without modification fails to produce deformations with many different local rotations. Recent research suggests that periodic functions are essential for coordinate MLPs to predict complex signals [47, 66, 74]. Periodic functions are usually used as positional encoding or activations of the form $\\sin ( a x + b )$ , where $a$ controls the frequency of the activation. To use such periodic function as part of the invertible residual block without restricting the frequency, we normalize the output of the periodic function $\\sin ( a x + b ) | a | ^ { - 1 }$ , bringing it is Lipschitz constant below 1. Formally, the positional encoding with normalized Lipschitz constant applied to one dimension is ", + "bbox": [ + 173, + 505, + 826, + 616 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/115f0ef27b3ae276645a06d8c15371d771109c767a72d8ffc95998a6ec1d55db.jpg", + "text": "$$\n\\gamma _ { i } ( { \\bf x } ) = \\frac { 1 } { \\sqrt { 2 L + 1 } } \\left( x _ { i } , \\frac { \\cos ( 2 ^ { 0 } \\pi { \\bf x } _ { i } ) } { 2 ^ { 0 } \\pi } , \\frac { \\sin ( 2 ^ { 0 } \\pi { \\bf x } _ { i } ) } { 2 ^ { 0 } \\pi } , \\ldots , \\frac { \\cos ( 2 ^ { L } \\pi { \\bf x } _ { i } ) } { 2 ^ { L } \\pi } , \\frac { \\sin ( 2 ^ { L } \\pi { \\bf x } _ { i } ) } { 2 ^ { L } \\pi } \\right) .\n$$", + "text_format": "latex", + "bbox": [ + 214, + 626, + 784, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We will apply such encoding to each of the dimensions of the input coordinate for the body of the invertible residual block: $\\begin{array} { r } { \\bar { R _ { \\theta } } ( \\mathbf { x } ) = \\mathbf { x } + g _ { \\theta } \\left( \\frac { 1 } { \\sqrt { d } } [ \\gamma _ { 1 } \\left( \\mathbf { x } \\right) , \\mathbf { \\Omega } , \\mathbf { \\Omega } . . . , \\gamma _ { d } \\left( \\mathbf { \\bar { x } } \\right) ] \\right) } \\end{array}$ . ", + "bbox": [ + 173, + 671, + 825, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ablation. We conduct ablation studies on two architecture choices: invertibility and positional encoding. In this experiment, we deform a neural field representing the SDF of a 2D rectangle. We optimize each ablation case to satisfies the user specified constraints with following loss: $\\begin{array} { r } { \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\left\\| D _ { \\theta } ( \\mathbf { h } _ { i } ) - \\mathbf { t } _ { i } \\right\\| ^ { 2 } } \\end{array}$ . The results are shown in Figure 4. If we replace the invertible architecture with SIREN as done in Deng et al. [25], the deformation field will tend to break topology (No inverse). Removing the positional encoding will fail to create a complex field (No $P E _ { \\mathrm { { \\ell } } }$ ). Our architecture can create a reasonable guess (No loss). This shows that our network architecture prioritizes natural deformation that preserves topology. ", + "bbox": [ + 174, + 729, + 549, + 911 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/513a5400ffef192f910dfe03539db2c361a75645844fec54771cf23c63e7d2b7.jpg", + "image_caption": [ + "Figure 4: Architecture ablation on 2D SDF deformation. Blue points are handles; Red points are targets. " + ], + "image_footnote": [], + "bbox": [ + 562, + 732, + 808, + 818 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3 Implicit Thin Shell Loss ", + "text_level": 1, + "bbox": [ + 174, + 90, + 380, + 106 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "At this point, we have obtained the correspondences $\\mathbf { y } = D _ { \\theta } ( \\mathbf { x } )$ , with $\\mathbf { x }$ in the output (or deformed) space and y in the input space. Our next step is to design $\\mathcal { L } _ { d f m }$ that compares these corresponding patches to ensure natural deformation. Recall that one way to ensure a natural-looking deformation is to minimize the amount the resistance to bending or stretching that happened during the deformation [1, 70]. We will develop novel loss functions for measuring stretching and bending. Please refer to the supplement for the connection between our loss and the thin shell energy. ", + "bbox": [ + 173, + 116, + 826, + 200 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3.1 Stretching Loss ", + "text_level": 1, + "bbox": [ + 174, + 214, + 333, + 229 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Stretching can be captured by the change of dot product in tangent space. Intuitively, a local surface patch is stretched when the lengths of some tangent vectors change. The change of tangent vectors’ norm can be measured by the tangent dot-product. With this said, the amount of stretch can be measured by the change of tangent dot product. ", + "bbox": [ + 174, + 237, + 825, + 294 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Note that we do not have access to analytical surface parameterization, so we need to express the tangent dot product with neural fields and its derivative. We can describe the tangent dot product to the spatial dot product using the projection matrix. The tangent vector of $\\mathbf { x }$ can be parameterized by projecting a vector $\\mathbf { v }$ to the tangent space. To achieve that, we need to multiply $\\mathbf { v }$ with the projection matrix $\\bar { \\mathbf { P } _ { G _ { \\theta } } } ( \\mathbf { x } ) = \\mathbf { I } - \\mathbf { n } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { \\bar { n } } _ { G _ { \\theta } } ( \\mathbf { \\bar { x } } ) ^ { T }$ , where $\\mathbf { n } _ { G _ { \\theta } } ( \\mathbf { x } )$ is the surface normal of point $\\mathbf { x }$ . $\\mathbf { \\bar { P } } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v }$ is a tangent vector in the tangent plane of $\\mathbf { x }$ . ", + "bbox": [ + 173, + 299, + 825, + 383 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Now we are ready to compute the change of tangent dot-product. Let $\\mathbf { t } _ { i }$ and $\\mathbf { t } _ { j }$ be two arbitrary tangent vectors near point $\\mathbf { x }$ at the deformed shape. Further assume that these vectors can be parameterized as $\\mathbf { t } _ { i } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { 1 }$ and $\\mathbf { t } _ { j } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { 2 }$ . These tangent vector will be transformed by $D _ { \\theta }$ into $\\mathbf { t } _ { i } ^ { \\prime } = \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { t } _ { i }$ and $\\mathbf { t } _ { j } ^ { \\prime } = \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { \\bar { x } } ) \\mathbf { t } _ { j }$ . These are tangent vectors at point $\\mathbf { y }$ at the input shape. The change of tangent dot-product with respect to these two vectors can be computed as follows: ", + "bbox": [ + 173, + 388, + 825, + 459 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/55ae1d4778cf1a5b605b4f6ba8167ec34cdc7a7d659dad5a3652492fa3cd586b.jpg", + "text": "$$\n\\begin{array} { r } { \\vert \\mathbf { t } _ { 1 } ^ { T } \\mathbf { t } _ { 2 } - \\mathbf { t } _ { 1 } ^ { \\prime T } \\mathbf { t } _ { 2 } ^ { \\prime } \\vert = \\vert \\mathbf { v } _ { 1 } ^ { T } \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) ^ { T } \\left( \\mathbf { I } - \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) ^ { T } \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\right) \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { 2 } \\vert . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 271, + 465, + 725, + 486 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To minimize the stretch, we need to enforce that dot-product stays the same for all tangent vectors. This can be done by minimize the matrix norm of $\\mathbf { \\dot { P } } _ { G _ { \\theta } } ^ { T } \\bigl ( \\mathbf { I } - \\mathbf { \\dot { J } } _ { D _ { \\theta } } ^ { T } \\mathbf { J } _ { D _ { \\theta } } \\bigr ) \\mathbf { P } _ { G _ { \\theta } }$ . Here, we drop the function arguments $\\mathbf { x }$ for the matrix for notation clarity. With these, we define the the stretch loss as: ", + "bbox": [ + 173, + 491, + 826, + 534 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/17478aacfa0825c24d4efefdcc10b097ca24f3d4fdf4bc8e89046ebe7f0b15a8.jpg", + "text": "$$\n\\mathcal { L } _ { s } ( G _ { \\theta } ) = \\int _ { \\mathbf { x } \\in \\mathcal { M } _ { G _ { \\theta } } } \\left. \\mathbf { P } _ { G _ { \\theta } } ^ { T } \\left( \\mathbf { I } - \\mathbf { J } _ { D _ { \\theta } } ^ { T } \\mathbf { J } _ { D _ { \\theta } } \\right) \\mathbf { P } _ { G _ { \\theta } } \\right. _ { F } ^ { 2 } d \\mathbf { x } .\n$$", + "text_format": "latex", + "bbox": [ + 320, + 537, + 676, + 575 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3.2 Bending Loss ", + "text_level": 1, + "bbox": [ + 173, + 587, + 320, + 603 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Bending can be characterized by the change of surface curvature (e.g., making the surface more or less curved). Intuitively, curvature can be described as the change of tangent dot product along the surface normal direction [16, 59]. Let $\\mathbf { t } _ { 1 } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { 1 }$ and $\\mathbf { t } _ { 2 } = \\mathbf { \\bar { P } } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { \\bar { v } } _ { 2 }$ be two tangent vectors at $\\mathbf { x }$ . Consider the tangent dot product of the surface family $\\mathbf { x } + t \\mathbf { n } ( \\mathbf { x } )$ . Note that this set of surface corresponding to the level sets ${ \\bf \\dot { \\{ p \\vert } } G _ { \\theta } ( { \\bf p } ) = t \\}$ if $G _ { \\theta }$ is approximating an SDF [54]. Then the change of dot product along the surface normal direction can be given by Hessian and directional derivative: $\\begin{array} { r } { \\frac { d } { d t } \\mathbf { t } _ { 1 } ^ { T } \\mathbf { t } _ { 2 } \\mathbf { \\bar { \\Psi } } _ { t = 0 } = \\mathbf { t } _ { 1 } ^ { T } \\bar { H _ { G _ { \\theta } } } ( \\mathbf { x } ) \\mathbf { t } _ { 2 } } \\end{array}$ . Intuitively, the larger this value is, the faster the surface changes whenmal direction, which means the surface has larger curvature. ", + "bbox": [ + 173, + 611, + 825, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Measuring bending amounts to measure the change of tangent dot-product derivative along the surface normal direction. Similar to the previous section, assume we have tangent vectors $\\mathbf { t } _ { i } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { i }$ and $\\mathbf { t } _ { j } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { j }$ . These tangent vectors are are transformed by the Jacobian of the deformation field $\\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } )$ to $\\dot { \\mathbf { t } } _ { i } ^ { \\prime } = \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { t } _ { i }$ and $\\mathbf { t } _ { j } ^ { \\prime } = \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { t } _ { j }$ . Since $\\mathbf { t } _ { i } ^ { \\prime }$ and $\\mathbf { t } _ { j } ^ { \\prime }$ are tangent vectors at point $\\mathbf { y }$ on the surface $\\mathcal { M } _ { F }$ , the derivative of tangent dot-product is given by the hessian matrix of field $F$ $: \\mathbf { \\Gamma } _ { d t } ^ { d } \\mathbf { t } _ { 1 } ^ { \\prime T } \\mathbf { t } _ { 2 } ^ { \\prime } | _ { t = 0 } = \\mathbf { t } _ { 1 } ^ { \\prime T } H _ { F } ( D _ { \\theta } ( \\mathbf { x } ) ) \\mathbf { t } _ { 2 } ^ { \\prime } = \\mathbf { t } _ { 1 } ^ { T } \\mathbf { J } _ { D _ { \\theta } } ^ { T } ( \\mathbf { x } ) H _ { F } ( D _ { \\theta } ( \\mathbf { x } ) ) \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { t } _ { 2 } .$ . We will drop the function argument to $\\mathbf { J } _ { D _ { \\theta } }$ , $H _ { G _ { \\theta } }$ , and $\\mathbf { P } _ { G _ { \\theta } }$ for notation clarity. The change of tangent dot-product derivative is: ", + "bbox": [ + 173, + 729, + 825, + 829 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/be54971a5a60e73bdcd5debb0fd63cc7fee4f4a5f165a9cbfea5a89a4ff84aef.jpg", + "text": "$$\n\\left| \\frac { d } { d t } \\left( \\mathbf { t } _ { 1 } ^ { T } \\mathbf { t } _ { 2 } - \\mathbf { t } _ { 1 } ^ { \\prime T } \\mathbf { t } _ { 2 } ^ { \\prime } \\right) _ { t = 0 } \\right| = \\left| \\mathbf { v } _ { 1 } ^ { T } \\mathbf { P } _ { G _ { \\theta } } ^ { T } \\left( H _ { G _ { \\theta } } - \\mathbf { J } _ { D _ { \\theta } } ^ { T } H _ { F } ( D _ { \\theta } ( \\mathbf { x } ) ) \\mathbf { J } _ { D _ { \\theta } } \\right) \\mathbf { P } _ { G _ { \\theta } } \\mathbf { v } _ { 2 } \\right| .\n$$", + "text_format": "latex", + "bbox": [ + 243, + 834, + 753, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "If there is almost no bending happened between the infinitesimal patches around $\\mathbf { x }$ and $\\mathbf { y }$ , then the quantity $\\begin{array} { r } { \\left| \\frac { d } { d t } \\left( \\mathbf { t } _ { 1 } ^ { T } \\mathbf { t } _ { 2 } - \\mathbf { t } _ { 1 } ^ { \\prime T } \\bar { \\mathbf { t } } _ { 2 } ^ { \\prime } \\right) _ { t = 0 } \\right| } \\end{array} \\qquad = 0 .$ should stay close to 0 for all pairs of tangent vectors. We will ", + "bbox": [ + 173, + 881, + 825, + 914 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "quantify this by the matrix norm of ${ \\bf P } _ { G _ { \\theta } } ^ { T } \\left( H _ { G _ { \\theta } } - { \\bf J } _ { D _ { \\theta } } ^ { T } H _ { F } ( D _ { \\theta } ( { \\bf x } ) ) { \\bf J } _ { D _ { \\theta } } \\right) { \\bf P } _ { G _ { \\theta } }$ . Finally, we arrive at our bending loss, which minimizes the norm of the matrix that modulate the change of tangent dot-product derivatives moving along the surface normal direction: ", + "bbox": [ + 174, + 89, + 825, + 133 + ], + "page_idx": 7 + }, + { + "type": "equation", + "img_path": "images/4c7abbcefd81e5539f2afe9b7ebd263d1d3dd8f74fe71abb5984c212b541028f.jpg", + "text": "$$\n\\mathcal { L } _ { b } ( G _ { \\theta } ) = \\int _ { x \\in \\mathcal { M } _ { G _ { \\theta } } } \\left\\| \\mathbf { P } _ { G _ { \\theta } } ^ { T } \\left( H _ { G _ { \\theta } } - \\mathbf { J } _ { D _ { \\theta } } ^ { T } H _ { F } ( D _ { \\theta } ( \\mathbf { x } ) ) \\mathbf { J } _ { D _ { \\theta } } \\right) \\mathbf { P } _ { G _ { \\theta } } \\right\\| _ { F } ^ { s } d \\mathbf { x } .\n$$", + "text_format": "latex", + "bbox": [ + 269, + 133, + 728, + 170 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3.3 Computing $\\mathcal { L } _ { s }$ and $\\mathcal { L } _ { b }$ ", + "text_level": 1, + "bbox": [ + 174, + 178, + 379, + 193 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Computing $\\mathcal { L } _ { s }$ and $\\mathcal { L } _ { b }$ during training requires approximating a surface integral of the form $\\begin{array} { r } { \\int _ { \\mathbf { x } \\in \\mathcal { M } _ { G _ { \\theta } } } \\bar { \\mathcal { L } } ( \\mathbf { x } ) d \\mathbf { x } } \\end{array}$ using Monte Carlo integration, which requires an efficient way to sample points θuniformly from surface $\\mathcal { M } _ { G _ { \\theta } }$ . While it is feasible to sample uniformly from an SDF, this is challenging to do with $G _ { \\theta }$ since there is no guarantee that $G _ { \\theta }$ remains a valid SDF during the course of training. Thanks to the invertibility of $D _ { \\theta }$ , we can apply change of variable $\\mathbf { x } = D _ { \\theta } ^ { - 1 } ( \\mathbf { y } )$ to the integration, where $\\mathbf { y }$ are points on the input surface $\\mathcal { M } _ { F }$ : ", + "bbox": [ + 173, + 200, + 825, + 290 + ], + "page_idx": 7 + }, + { + "type": "equation", + "img_path": "images/e2899c8e60314aa5d0d262add3c4d68fbf158450ae273c1e944f406c27384e93.jpg", + "text": "$$\n\\int _ { \\mathbf { x } \\in \\mathcal { M } _ { G _ { \\theta } } } \\mathcal { L } ( \\mathbf { x } ) d \\mathbf { x } = \\int _ { \\mathbf { y } \\in \\mathcal { M } _ { F } } \\mathcal { L } ( \\mathbf { x } ) \\left| \\operatorname* { d e t } \\left( \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) + \\mathbf { n } _ { F } ( \\mathbf { y } ) \\mathbf { n } _ { G _ { \\theta } } ( \\mathbf { x } ) ^ { T } \\right) \\right| ^ { - 2 } d \\mathbf { y } .\n$$", + "text_format": "latex", + "bbox": [ + 222, + 291, + 776, + 327 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$\\mathbf { J } _ { D _ { \\theta } } \\mathbf { P } _ { G _ { \\theta } } \\in \\mathbb { R } ^ { 3 \\times 3 }$ maps tangent vector from $\\mathcal { M } _ { G _ { \\theta } }$ to $\\mathcal { M } _ { F }$ . We apply the extension trick from Iglesias et al. [35] to create a matrix whose determinant equals the change of surface area. This is achieved by adding the surface normal component $\\mathbf { n } _ { F } \\mathbf { n } _ { G } ^ { T }$ and keeping it unchanged. With this change of variable, we now can compute the losses with point samples from the input field $F$ . Since the input field $F$ approximates an SDF, we can use the method introduced in Section 5.1 to sample uniform points. ", + "bbox": [ + 173, + 329, + 825, + 400 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4 Optimization ", + "text_level": 1, + "bbox": [ + 173, + 414, + 305, + 429 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Putting the losses together, we deform a neural field by solving the constrained optimization problem ", + "bbox": [ + 176, + 439, + 823, + 454 + ], + "page_idx": 7 + }, + { + "type": "equation", + "img_path": "images/bc7131e80976def89d777867f865510168603474709b0e2f96c867263c85bc6b.jpg", + "text": "$$\n\\underset { \\theta } { \\arg \\operatorname* { m i n } } \\lambda _ { s } \\mathcal { L } _ { s } ( G _ { \\theta } ) + \\lambda _ { b } \\mathcal { L } _ { b } ( G _ { \\theta } ) , \\quad \\mathrm { s . t . } \\forall 1 \\leq i \\leq n , \\ \\| D _ { \\theta } ( \\mathbf { t } _ { i } ) - \\mathbf { h } _ { i } \\| = 0\n$$", + "text_format": "latex", + "bbox": [ + 258, + 455, + 736, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $\\lambda _ { s } , \\lambda _ { b }$ are hyperparameters that determine the material properties. One way to solve this constrained optimization problem for a neural network is to make the constraints a soft loss adding to the objective function: $\\begin{array} { r } { \\dot { \\mathcal { L } } _ { c o n s t } ^ { { \\bf \\Delta } } ( D _ { \\theta } ) = \\frac { 1 } { n } \\sum _ { 1 = 1 } ^ { n } \\left. D _ { \\theta } ( \\mathbf { t } _ { i } ) - \\mathbf { h } _ { i } \\right. } \\end{array}$ . Our final objective is: ", + "bbox": [ + 174, + 481, + 825, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We set $\\lambda _ { c }$ to be a high value to enforce that the model satisfies user-specified input as much as possible. The user can tune $\\lambda _ { b }$ and $\\lambda _ { s }$ depending on the application scenario. We optimize $\\mathcal { L } ( \\boldsymbol { \\theta } )$ with Adam optimizer to obtain the output field $G _ { \\theta }$ . Hyperparameters are provided in the supplement. ", + "bbox": [ + 173, + 545, + 825, + 587 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6 Deformation Results ", + "text_level": 1, + "bbox": [ + 174, + 604, + 377, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we will demonstrate the results of our methods to shape deformation. The shapes for deformation are taken from Sorkine-Hornung and Alexa [70]. To create neural fields from these meshes, we follow the procedure of Park et al. [56] to compute ground-truth SDF for locations sampled within $[ - 1 , 1 ] ^ { 3 }$ . We then fit a SIREN [66] to the ground-truth SDF to generate our initial neural fields. Our main baseline is ARAP [70, 86]. The simplest way to use ARAP to edit neural fields is applying it on a mesh extracted from the input neural fields using marching cubes [44, 45]. We first present results comparing with ARAP applied to the extracted mesh. Then we will conduct an analysis to show our losses encourage the right behaviors. ", + "bbox": [ + 173, + 633, + 825, + 746 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparing to ARAP baseline. We follow ARAP [70] to create a set of basic shape deformation operations to evaluate our algorithm. In this setting, the user will first specify a set of handles used for manipulation (shown in Figure 5 in blue). In general, the user can apply three basic types of operation on a handle: 1) make it static (i.e., no deformation), 2) translate it, or 3) rotate it around a center. Usually, the first operation is used in combination with the latter two to produce useful deformation. We first show how our algorithm deforms simple objects (e.g., a cylinder and a rectangle bar) when the user rotates or translates one end while fixing the other. We then extend this set of operations to shapes with more detail (e.g., Cactus, Armadillo, and Dino). Finally, we test our algorithms when all three operations are specified together on a single shape. The results are shown in Figure 5. We can see that applying ARAP directly on the extracted mesh creates undesirable volume distortion. Our algorithm is able to produce deformation results that are natural while satisfying the user’s intention. ", + "bbox": [ + 173, + 758, + 825, + 911 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4b0800ba8a5e03bd4ddc57775de98cce018d0745cceb87a6a5d10c6b16f46363.jpg", + "image_caption": [ + "Figure 5: Deformation results. (A) Input shape. (B) Baseline. (C) Ours. Red points are user specified handles $\\mathbf { h } _ { i }$ . Blue points denote user specified target points $\\mathbf { t } _ { i }$ . First row: single rotation or translation on simple shapes. Second and third rows: single rotation or translation on more complex objects. Fourth row: multiple edits on complex objects. " + ], + "image_footnote": [], + "bbox": [ + 173, + 92, + 823, + 549 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Comparing to different ARAP variants. This artifact is partially due to the surface discretization made by the marching cubed algorithm doesn’t agree with the assumptions made by ARAP [41]. To verify this hypothesis, we also include three additional baselines in Figure 6. First, we show the results of applying ARAP on the low-poly mesh used to create the input neural fields (Original). Second, we first apply Garland and Heckbert [28] to simplify the surface of the extracted mesh before applying ARAP to it (Remeshed). Finally, we also compare to the results of SR-ARAP [41], which adds smoothness regularization to ARAP to remove some unnatural distortion (SR-ARAP). The figure shows that ARAP works much better when the surface is discretized appropriately. Discretizing the surface, however, usually requires case-by-case manual adjustment to perform well. Our algorithm does not suffer from such issues as we optimize the thin shell objective directly without committing to a particular discretization of the surface. ", + "bbox": [ + 174, + 631, + 825, + 784 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Loss analysis. Here we provide an experiment to analyze the behavior of stretching loss and bending loss. Specifically, we compare models optimized for only the stretching loss $\\mathcal { L } _ { s }$ , only the bending loss $\\mathcal { L } _ { b }$ , and both losses together. Similar to Section 5.2, we deform a neural field that approximates the SDF of a 2D rectangle. The results are shown in Figure 7. Optimizing only for $\\mathcal { L } _ { s }$ produces a shape that best preserves surface area (or the perimeter in the 2D case), which explains the wiggling. Optimizing only for $\\mathcal { L } _ { b }$ produces a shape that tries to prevent wiggling of the surface, which changes the curvature of the surface. The user can choose appropriate $\\lambda _ { s }$ and $\\lambda _ { b }$ to produce deformation with resistance to both bending and stretching. ", + "bbox": [ + 174, + 800, + 825, + 911 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/2de287fec84c55f2a62835e84347ec2e58c183b03740c6cd0bb69c78658d3bc9.jpg", + "image_caption": [ + "Figure 6: Additional ARAP baselines. Directly applying ARAP to extracted mesh produces poor results (i.e., MC). While this can be alleviated by remshing (i.e. Original or Remeshed) or regularization (i.e. SR-ARAP), this shows mesh deformation algorithms can be sensitive to discretization quality. Our method do not discretize the surface, thus circumvent such issue. Red points are handles; Blue points are targets. " + ], + "image_footnote": [], + "bbox": [ + 196, + 85, + 799, + 208 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "7 Discussion, Limitations, and Future work ", + "text_level": 1, + "bbox": [ + 174, + 308, + 550, + 325 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Advantages of using neural fields for geometry processing. The main strength of using neural fields for geometry processing is that one can disentangle the processing algorithm from the surface discretization. Users do not need to worry about discretization while manipulating a shape represented in neural fields. This might open the door to more automatic geometry processing pipelines. Additionally, neural fields are modular and can be combined with other neural networks. Neural fields can be easily incorporated into current deep learning pipelines. This makes them well-suited for data-driven applications. ", + "bbox": [ + 174, + 339, + 550, + 491 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/019673aff3153b24234a310391ed42d9c81088591fddf2cc7eb418d921800332.jpg", + "image_caption": [ + "Figure 7: Analysis of stretching and bending losses. Blue points are handles; Red points are targets. " + ], + "image_footnote": [], + "bbox": [ + 575, + 348, + 808, + 433 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Limitations and future directions. The main limitation of our method is the slow optimization speed that hinders interactive editing. Typically, ARAP can solve each of such deformation problems within half an hour for large meshes, and it can achieve interactive speed for meshes with a small number of triangles. The Taubin smoothing can finish in a couple of seconds. Our deformation method right now requires a TitanX GPU with 12GB memory to train for 10 hours. Our smoothing and sharpening method takes about 10 minutes on the same GPU. The current algorithm does not ensure that the output field remains an SDF, which prevents performing multiple editing operations. ", + "bbox": [ + 173, + 500, + 825, + 597 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "We believe many of these limitations can be addressed in future work. One can potentially use techniques like progressive training or meta-learning [67, 75] to improve the training speed. To allow consecutive editing, we can design regularization loss that enforces the output fields to approximate an SDF [4] or design sampling methods robust with noisy SDF. Other interesting directions include providing deeper theoretical analysis and applying neural fields in other geometry processing tasks. ", + "bbox": [ + 174, + 603, + 825, + 672 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Societal impact. Our work can lead to more efficient geometry processing algorithms. Such algorithms can empower artists to generate creative content. Potential negative impact includes misuse of geometry processing algorithms to create offensive content. ", + "bbox": [ + 176, + 681, + 823, + 723 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "8 Conclusion ", + "text_level": 1, + "bbox": [ + 174, + 742, + 299, + 760 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Our work provides a proof of concept that geometry processing can be done entirely with neural fields without discretizing the surface. We develop network architectures and training objectives for filtering and deforming shapes represented by neural fields and demonstrate the advantages of using neural fields for geometry processing. We hope that our work can inspire a new generation of geometry processing algorithms using neural fields. ", + "bbox": [ + 174, + 773, + 825, + 843 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Acknowledgement. Guandao’s PhD was supported in part by a research gift from Magic Leap and a donation from NVIDIA. We want to thank Wenqi Xian, Professor Steve Marschner, and members of Intel Labs for providing insightful feedback for this project. ", + "bbox": [ + 174, + 852, + 821, + 893 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "References [1] M. Alexa, D. Cohen-Or, and D. Levin. As-rigid-as-possible shape interpolation. Proceedings of the 27th annual conference on Computer graphics and interactive techniques, 2000. 5, 7 [2] Pierre Alliez, Mark Meyer, and Mathieu Desbrun. Interactive geometry remeshing. ACM Transactions on Graphics (TOG), 21(3):347–354, 2002. 1 [3] Pierre Alliez, David Cohen-Steiner, Olivier Devillers, Bruno Lévy, and Mathieu Desbrun. Anisotropic polygonal remeshing. ACM SIGGRAPH 2003 Papers, 2003. 1 [4] Matan Atzmon and Y. Lipman. 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We introduce loss", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 335, + 469, + 348 + ], + "spans": [ + { + "bbox": [ + 141, + 335, + 469, + 348 + ], + "score": 1.0, + "content": "functions and architectures to show that some of the most challenging geometry", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 347, + 471, + 358 + ], + "spans": [ + { + "bbox": [ + 141, + 347, + 471, + 358 + ], + "score": 1.0, + "content": "processing tasks, such as deformation and filtering, can be done with neural fields.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 142, + 358, + 470, + 369 + ], + "spans": [ + { + "bbox": [ + 142, + 358, + 470, + 369 + ], + "score": 1.0, + "content": "Experimental results show that our methods are on par with the well-established", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 142, + 368, + 470, + 380 + ], + "spans": [ + { + "bbox": [ + 142, + 368, + 470, + 380 + ], + "score": 1.0, + "content": "mesh-based methods without committing to a particular surface discretization.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 142, + 379, + 424, + 391 + ], + "spans": [ + { + "bbox": [ + 142, + 379, + 424, + 391 + ], + "score": 1.0, + "content": "Code is available at https://github.com/stevenygd/NFGP.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 16.5 + }, + { + "type": "title", + "bbox": [ + 107, + 415, + 190, + 428 + ], + "lines": [ + { + "bbox": [ + 105, + 414, + 192, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 414, + 192, + 431 + ], + "score": 1.0, + "content": "1 Introduction", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 442, + 505, + 551 + ], + "lines": [ + { + "bbox": [ + 105, + 441, + 505, + 454 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 505, + 454 + ], + "score": 1.0, + "content": "In many graphics applications, users may want to edit digital shapes using just a few clicks, such", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 453, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 505, + 465 + ], + "score": 1.0, + "content": "as making a character bow by dragging the head downwards. Such manipulation from sparse input", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 464, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 506, + 477 + ], + "score": 1.0, + "content": "requires geometry processing algorithms. Most of these algorithms use polygonal meshes to represent", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 474, + 506, + 487 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 506, + 487 + ], + "score": 1.0, + "content": "shapes [11]. Polygonal meshes were created initially for researchers as a representation of real-world", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 485, + 506, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 485, + 506, + 498 + ], + "score": 1.0, + "content": "shapes that they can both interpret and manipulate [14, 52, 78]. 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The community", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 642, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 506, + 657 + ], + "score": 1.0, + "content": "has achieved compelling results using neural fields in a variety of applications [47, 64, 73, 84].", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "Notwithstanding these results, it is still unclear whether shape editing tasks challenging for implicit", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "fields (e.g., deformation and filtering) can be performed with neural fields. 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Given that", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 529, + 504, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 504, + 542 + ], + "score": 1.0, + "content": "shape editing is increasingly performed by algorithms, it seems worthwhile to search for a shape", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 539, + 396, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 539, + 396, + 554 + ], + "score": 1.0, + "content": "representation that is more amenable to automatic geometry processing.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 29.5, + "bbox_fs": [ + 105, + 441, + 506, + 554 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 556, + 505, + 687 + ], + "lines": [ + { + "bbox": [ + 105, + 555, + 505, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 505, + 569 + ], + "score": 1.0, + "content": "An alternative to the polygonal mesh is an implicit representation, in which the surface is represented", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 104, + 566, + 506, + 582 + ], + "spans": [ + { + "bbox": [ + 104, + 566, + 203, + 582 + ], + "score": 1.0, + "content": "by a level set of a field:", + "type": "text" + }, + { + "bbox": [ + 203, + 567, + 259, + 579 + ], + "score": 0.92, + "content": "\\bar { \\{ x \\vert f ( x ) = c \\} }", + "type": "inline_equation" + }, + { + "bbox": [ + 260, + 566, + 506, + 582 + ], + "score": 1.0, + "content": "[22, 39, 63]. Since it is easy to change shape topology using", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 578, + 505, + 591 + ], + "spans": [ + { + "bbox": [ + 106, + 578, + 505, + 591 + ], + "score": 1.0, + "content": "implicit representations, people have applied them for geometry processing tasks such as shape", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 588, + 505, + 602 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 505, + 602 + ], + "score": 1.0, + "content": "merging [8, 51, 54]. These works store implicit fields using voxels or octrees, which introduce", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 600, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 600, + 505, + 612 + ], + "score": 1.0, + "content": "memory-intensive spatial discretization. Recent research addresses this by using continuous neural", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 611, + 506, + 623 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 506, + 623 + ], + "score": 1.0, + "content": "networks to represent implicit fields [19, 45, 46, 56]. These neural fields possess several advantages", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 622, + 504, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 504, + 634 + ], + "score": 1.0, + "content": "in addition to the merits inherited from implicit representation: they are compact to store [23, 45]", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 632, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 646 + ], + "score": 1.0, + "content": "and can produce high-quality continuous surfaces at arbitrary resolutions [45, 56]. The community", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 642, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 506, + 657 + ], + "score": 1.0, + "content": "has achieved compelling results using neural fields in a variety of applications [47, 64, 73, 84].", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "Notwithstanding these results, it is still unclear whether shape editing tasks challenging for implicit", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "fields (e.g., deformation and filtering) can be performed with neural fields. In this paper, we ask: can", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 677, + 338, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 338, + 689 + ], + "score": 1.0, + "content": "geometry processing be done entirely using neural fields?", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 40.5, + "bbox_fs": [ + 104, + 555, + 506, + 689 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 193 + ], + "lines": [ + { + "bbox": [ + 105, + 73, + 505, + 86 + ], + "spans": [ + { + "bbox": [ + 105, + 73, + 505, + 86 + ], + "score": 1.0, + "content": "Geometry processing tasks are challenging because they are typically under-constrained: user input", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 84, + 507, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 84, + 507, + 96 + ], + "score": 1.0, + "content": "is very sparse. Therefore, we need to leverage priors that characterize how a natural surface behaves.", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "score": 1.0, + "content": "Such surface priors are usually instantiated by minimizing energy functionals that describe the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 106, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 106, + 505, + 118 + ], + "score": 1.0, + "content": "physical properties of surfaces using operators from differential geometry. For example, one can", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 116, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 506, + 128 + ], + "score": 1.0, + "content": "encourage surfaces to be smooth by minimizing the curvature, which can be measured by the Laplace-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 127, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 506, + 141 + ], + "score": 1.0, + "content": "Beltrami operator. Such operators, however, require a parameterization of the surface, which is", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 137, + 505, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 505, + 151 + ], + "score": 1.0, + "content": "not available for level sets of a neural field. Mesh algorithms usually approximate these geometric", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 149, + 506, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 506, + 162 + ], + "score": 1.0, + "content": "operators using the geodesic neighbors of the surface point. This allows the algorithms to focus on", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 159, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 505, + 173 + ], + "score": 1.0, + "content": "intrinsic geometric properties that are independent of shape parameterization. However, it is not easy", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 171, + 506, + 184 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 506, + 184 + ], + "score": 1.0, + "content": "to obtain geodesic neighbors in a neural field since the surface of interest is encoded implicitly by a", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 182, + 355, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 355, + 194 + ], + "score": 1.0, + "content": "set of points that evaluate the field function to the same value.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 198, + 505, + 297 + ], + "lines": [ + { + "bbox": [ + 106, + 199, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 106, + 199, + 505, + 210 + ], + "score": 1.0, + "content": "We posit that computing these geometric operators in neural fields requires a fundamentally different", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "score": 1.0, + "content": "approach. The idea is to approximate the local surface of the level set using the derivatives of the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 220, + 507, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 507, + 233 + ], + "score": 1.0, + "content": "underlying field. We can evaluate intrinsic geometry properties of the level set, such as curvature,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 230, + 506, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 506, + 244 + ], + "score": 1.0, + "content": "using only the field derivatives [39, 54]. This allows us to develop loss functions that describe surface", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 241, + 506, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 506, + 254 + ], + "score": 1.0, + "content": "priors such as elasticity or rigidity. To achieve this, we use the fact that neural fields are designed to", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 252, + 505, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 505, + 265 + ], + "score": 1.0, + "content": "be infinitely differentiable [66, 74]. The infinite differentiability of neural fields makes it possible to", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 263, + 507, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 263, + 507, + 277 + ], + "score": 1.0, + "content": "optimize loss functions that involve higher-order derivatives using gradient descent methods. Thus,", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 274, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 506, + 288 + ], + "score": 1.0, + "content": "unlike mesh-based geometry processing algorithms that approximate these objectives using surface", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 285, + 424, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 424, + 298 + ], + "score": 1.0, + "content": "discretizations, we can directly optimize in terms of the derivatives of the field.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 302, + 505, + 401 + ], + "lines": [ + { + "bbox": [ + 105, + 300, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 300, + 505, + 316 + ], + "score": 1.0, + "content": "Our formulation provides a proof of concept that geometry processing can be done entirely using", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 313, + 505, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 326 + ], + "score": 1.0, + "content": "neural fields. In particular, we focus on two tasks: shape filtering (e.g., smoothing and sharpening) and", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 324, + 506, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 506, + 336 + ], + "score": 1.0, + "content": "topology-preserving deformations. These two tasks are not only essential for downstream applications", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 333, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 505, + 348 + ], + "score": 1.0, + "content": "but also bring out the known challenges associated with implicit representations. We first tackle shape", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 345, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 505, + 358 + ], + "score": 1.0, + "content": "sharpening and smoothing and show how these can be done by optimizing a loss function based on", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 356, + 506, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 506, + 370 + ], + "score": 1.0, + "content": "geometric properties computed via the neural field’s derivatives. To achieve shape deformation, we", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 367, + 506, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 506, + 380 + ], + "score": 1.0, + "content": "propose to warp the neural field using a deformation vector field modeled by an invertible neural", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 378, + 506, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 506, + 391 + ], + "score": 1.0, + "content": "network [7]. With this invertible deformation field, we derive a training objective that models the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 389, + 297, + 402 + ], + "spans": [ + { + "bbox": [ + 106, + 389, + 297, + 402 + ], + "score": 1.0, + "content": "implicitly represented surfaces as elastic shells.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 108, + 405, + 505, + 439 + ], + "lines": [ + { + "bbox": [ + 106, + 405, + 505, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 505, + 418 + ], + "score": 1.0, + "content": "We compare our method with well-established mesh-based baselines [70, 76]. Our method can match", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 416, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 505, + 429 + ], + "score": 1.0, + "content": "the quality of the mesh-based counterparts without discretizing the surface. We hope that our work", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 427, + 447, + 441 + ], + "spans": [ + { + "bbox": [ + 106, + 427, + 447, + 441 + ], + "score": 1.0, + "content": "can inspire future generations of geometry processing algorithms using neural fields.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30 + }, + { + "type": "title", + "bbox": [ + 107, + 453, + 197, + 467 + ], + "lines": [ + { + "bbox": [ + 105, + 452, + 198, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 198, + 469 + ], + "score": 1.0, + "content": "2 Related Work", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 108, + 478, + 504, + 511 + ], + "lines": [ + { + "bbox": [ + 106, + 478, + 506, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 506, + 491 + ], + "score": 1.0, + "content": "This paper builds on two bodies of work: polygon mesh geometry processing and neural field", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 489, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 506, + 502 + ], + "score": 1.0, + "content": "representations. We will focus on prior work on two geometry processing tasks: shape filtering and", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 499, + 453, + 514 + ], + "spans": [ + { + "bbox": [ + 106, + 499, + 453, + 514 + ], + "score": 1.0, + "content": "topology-preserving deformation. Please refer to Botsch et al. [11] for further reading.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 523, + 504, + 588 + ], + "lines": [ + { + "bbox": [ + 105, + 522, + 505, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 505, + 536 + ], + "score": 1.0, + "content": "Mesh smoothing (and sharpening). The goal of mesh smoothing is to remove high-frequency", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 533, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 505, + 546 + ], + "score": 1.0, + "content": "noise and produce a smooth surface. Noise removal can be achieved by Fourier analysis [76, 79]", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 544, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 505, + 558 + ], + "score": 1.0, + "content": "or by modeling surface motion with a diffusion equation [26]. Smoothness can be promoted by", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 556, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 506, + 568 + ], + "score": 1.0, + "content": "minimizing energy functionals inspired by differential operators [50, 72, 82]. Sharpening is the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 566, + 506, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 506, + 579 + ], + "score": 1.0, + "content": "inverse of smoothing. In this paper, we adopt the goal of smoothing from prior work [20, 76] and", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 577, + 364, + 590 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 364, + 590 + ], + "score": 1.0, + "content": "design a corresponding differentiable objective for neural fields.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 38.5 + }, + { + "type": "text", + "bbox": [ + 107, + 600, + 505, + 666 + ], + "lines": [ + { + "bbox": [ + 106, + 600, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 506, + 613 + ], + "score": 1.0, + "content": "Implicit field smoothing. Implicit representations can be smoothed by evolving the level set", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 611, + 506, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 506, + 624 + ], + "score": 1.0, + "content": "according to its curvature normal [49, 54]. Many network architectures, such as ReLU MLP,", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 622, + 506, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 506, + 635 + ], + "score": 1.0, + "content": "bias toward smoothness when modeling an implicit field [61, 66, 74]. Regularization objectives", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 634, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 634, + 505, + 645 + ], + "score": 1.0, + "content": "and initialization schemes have been proposed to obtain smooth level sets from scanned surface", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 644, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 656 + ], + "score": 1.0, + "content": "points [5, 31]. These works mostly use smoothness as a prior when training neural fields. Our work", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 655, + 448, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 448, + 667 + ], + "score": 1.0, + "content": "formulates an objective that allows smoothing or sharpening a neural field as desired.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 44.5 + }, + { + "type": "text", + "bbox": [ + 108, + 678, + 504, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 504, + 689 + ], + "score": 1.0, + "content": "Mesh deformation. Mesh deformation is done by either deforming the shape (i.e. vertices) [9, 69]", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 688, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 701 + ], + "score": 1.0, + "content": "or the space [6, 36, 41, 48, 65]. These algorithms usually draw inspiration from physics and", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 104, + 699, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 104, + 699, + 506, + 713 + ], + "score": 1.0, + "content": "differential geometry to develop energy functions that encourage natural deformation [10, 15, 24,", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "score": 1.0, + "content": "70, 71, 77]. They also linearize such objectives so that they can be solved efficiently using linear", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 49.5 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 742, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 741, + 310, + 753 + ], + "spans": [ + { + "bbox": [ + 301, + 741, + 310, + 753 + ], + "score": 1.0, + "content": "2", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 193 + ], + "lines": [ + { + "bbox": [ + 105, + 73, + 505, + 86 + ], + "spans": [ + { + "bbox": [ + 105, + 73, + 505, + 86 + ], + "score": 1.0, + "content": "Geometry processing tasks are challenging because they are typically under-constrained: user input", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 84, + 507, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 84, + 507, + 96 + ], + "score": 1.0, + "content": "is very sparse. Therefore, we need to leverage priors that characterize how a natural surface behaves.", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "score": 1.0, + "content": "Such surface priors are usually instantiated by minimizing energy functionals that describe the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 106, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 106, + 505, + 118 + ], + "score": 1.0, + "content": "physical properties of surfaces using operators from differential geometry. For example, one can", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 116, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 506, + 128 + ], + "score": 1.0, + "content": "encourage surfaces to be smooth by minimizing the curvature, which can be measured by the Laplace-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 127, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 506, + 141 + ], + "score": 1.0, + "content": "Beltrami operator. Such operators, however, require a parameterization of the surface, which is", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 137, + 505, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 505, + 151 + ], + "score": 1.0, + "content": "not available for level sets of a neural field. Mesh algorithms usually approximate these geometric", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 149, + 506, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 506, + 162 + ], + "score": 1.0, + "content": "operators using the geodesic neighbors of the surface point. This allows the algorithms to focus on", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 159, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 505, + 173 + ], + "score": 1.0, + "content": "intrinsic geometric properties that are independent of shape parameterization. However, it is not easy", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 171, + 506, + 184 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 506, + 184 + ], + "score": 1.0, + "content": "to obtain geodesic neighbors in a neural field since the surface of interest is encoded implicitly by a", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 182, + 355, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 355, + 194 + ], + "score": 1.0, + "content": "set of points that evaluate the field function to the same value.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 73, + 507, + 194 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 198, + 505, + 297 + ], + "lines": [ + { + "bbox": [ + 106, + 199, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 106, + 199, + 505, + 210 + ], + "score": 1.0, + "content": "We posit that computing these geometric operators in neural fields requires a fundamentally different", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "score": 1.0, + "content": "approach. The idea is to approximate the local surface of the level set using the derivatives of the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 220, + 507, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 507, + 233 + ], + "score": 1.0, + "content": "underlying field. We can evaluate intrinsic geometry properties of the level set, such as curvature,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 230, + 506, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 506, + 244 + ], + "score": 1.0, + "content": "using only the field derivatives [39, 54]. This allows us to develop loss functions that describe surface", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 241, + 506, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 506, + 254 + ], + "score": 1.0, + "content": "priors such as elasticity or rigidity. To achieve this, we use the fact that neural fields are designed to", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 252, + 505, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 505, + 265 + ], + "score": 1.0, + "content": "be infinitely differentiable [66, 74]. The infinite differentiability of neural fields makes it possible to", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 263, + 507, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 263, + 507, + 277 + ], + "score": 1.0, + "content": "optimize loss functions that involve higher-order derivatives using gradient descent methods. Thus,", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 274, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 506, + 288 + ], + "score": 1.0, + "content": "unlike mesh-based geometry processing algorithms that approximate these objectives using surface", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 285, + 424, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 424, + 298 + ], + "score": 1.0, + "content": "discretizations, we can directly optimize in terms of the derivatives of the field.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15, + "bbox_fs": [ + 105, + 199, + 507, + 298 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 302, + 505, + 401 + ], + "lines": [ + { + "bbox": [ + 105, + 300, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 300, + 505, + 316 + ], + "score": 1.0, + "content": "Our formulation provides a proof of concept that geometry processing can be done entirely using", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 313, + 505, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 326 + ], + "score": 1.0, + "content": "neural fields. In particular, we focus on two tasks: shape filtering (e.g., smoothing and sharpening) and", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 324, + 506, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 506, + 336 + ], + "score": 1.0, + "content": "topology-preserving deformations. These two tasks are not only essential for downstream applications", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 333, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 505, + 348 + ], + "score": 1.0, + "content": "but also bring out the known challenges associated with implicit representations. We first tackle shape", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 345, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 505, + 358 + ], + "score": 1.0, + "content": "sharpening and smoothing and show how these can be done by optimizing a loss function based on", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 356, + 506, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 506, + 370 + ], + "score": 1.0, + "content": "geometric properties computed via the neural field’s derivatives. To achieve shape deformation, we", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 367, + 506, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 506, + 380 + ], + "score": 1.0, + "content": "propose to warp the neural field using a deformation vector field modeled by an invertible neural", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 378, + 506, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 506, + 391 + ], + "score": 1.0, + "content": "network [7]. With this invertible deformation field, we derive a training objective that models the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 389, + 297, + 402 + ], + "spans": [ + { + "bbox": [ + 106, + 389, + 297, + 402 + ], + "score": 1.0, + "content": "implicitly represented surfaces as elastic shells.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 300, + 506, + 402 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 405, + 505, + 439 + ], + "lines": [ + { + "bbox": [ + 106, + 405, + 505, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 505, + 418 + ], + "score": 1.0, + "content": "We compare our method with well-established mesh-based baselines [70, 76]. Our method can match", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 416, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 505, + 429 + ], + "score": 1.0, + "content": "the quality of the mesh-based counterparts without discretizing the surface. We hope that our work", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 427, + 447, + 441 + ], + "spans": [ + { + "bbox": [ + 106, + 427, + 447, + 441 + ], + "score": 1.0, + "content": "can inspire future generations of geometry processing algorithms using neural fields.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30, + "bbox_fs": [ + 106, + 405, + 505, + 441 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 453, + 197, + 467 + ], + "lines": [ + { + "bbox": [ + 105, + 452, + 198, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 198, + 469 + ], + "score": 1.0, + "content": "2 Related Work", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 108, + 478, + 504, + 511 + ], + "lines": [ + { + "bbox": [ + 106, + 478, + 506, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 506, + 491 + ], + "score": 1.0, + "content": "This paper builds on two bodies of work: polygon mesh geometry processing and neural field", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 489, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 506, + 502 + ], + "score": 1.0, + "content": "representations. We will focus on prior work on two geometry processing tasks: shape filtering and", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 499, + 453, + 514 + ], + "spans": [ + { + "bbox": [ + 106, + 499, + 453, + 514 + ], + "score": 1.0, + "content": "topology-preserving deformation. Please refer to Botsch et al. [11] for further reading.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34, + "bbox_fs": [ + 106, + 478, + 506, + 514 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 523, + 504, + 588 + ], + "lines": [ + { + "bbox": [ + 105, + 522, + 505, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 505, + 536 + ], + "score": 1.0, + "content": "Mesh smoothing (and sharpening). The goal of mesh smoothing is to remove high-frequency", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 533, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 505, + 546 + ], + "score": 1.0, + "content": "noise and produce a smooth surface. Noise removal can be achieved by Fourier analysis [76, 79]", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 544, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 505, + 558 + ], + "score": 1.0, + "content": "or by modeling surface motion with a diffusion equation [26]. Smoothness can be promoted by", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 556, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 506, + 568 + ], + "score": 1.0, + "content": "minimizing energy functionals inspired by differential operators [50, 72, 82]. Sharpening is the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 566, + 506, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 506, + 579 + ], + "score": 1.0, + "content": "inverse of smoothing. In this paper, we adopt the goal of smoothing from prior work [20, 76] and", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 577, + 364, + 590 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 364, + 590 + ], + "score": 1.0, + "content": "design a corresponding differentiable objective for neural fields.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 522, + 506, + 590 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 600, + 505, + 666 + ], + "lines": [ + { + "bbox": [ + 106, + 600, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 506, + 613 + ], + "score": 1.0, + "content": "Implicit field smoothing. Implicit representations can be smoothed by evolving the level set", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 611, + 506, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 506, + 624 + ], + "score": 1.0, + "content": "according to its curvature normal [49, 54]. Many network architectures, such as ReLU MLP,", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 622, + 506, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 506, + 635 + ], + "score": 1.0, + "content": "bias toward smoothness when modeling an implicit field [61, 66, 74]. Regularization objectives", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 634, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 634, + 505, + 645 + ], + "score": 1.0, + "content": "and initialization schemes have been proposed to obtain smooth level sets from scanned surface", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 644, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 656 + ], + "score": 1.0, + "content": "points [5, 31]. These works mostly use smoothness as a prior when training neural fields. Our work", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 655, + 448, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 448, + 667 + ], + "score": 1.0, + "content": "formulates an objective that allows smoothing or sharpening a neural field as desired.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 44.5, + "bbox_fs": [ + 105, + 600, + 506, + 667 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 678, + 504, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 504, + 689 + ], + "score": 1.0, + "content": "Mesh deformation. Mesh deformation is done by either deforming the shape (i.e. vertices) [9, 69]", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 688, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 701 + ], + "score": 1.0, + "content": "or the space [6, 36, 41, 48, 65]. These algorithms usually draw inspiration from physics and", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 104, + 699, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 104, + 699, + 506, + 713 + ], + "score": 1.0, + "content": "differential geometry to develop energy functions that encourage natural deformation [10, 15, 24,", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "score": 1.0, + "content": "70, 71, 77]. They also linearize such objectives so that they can be solved efficiently using linear", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 106, + 73, + 504, + 84 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 504, + 84 + ], + "score": 1.0, + "content": "solvers [9]. Recent research also applies deep learning to optimize for non-linear deformation", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "score": 1.0, + "content": "losses [32, 34, 38, 80, 81, 83]. Deforming a mesh, however, requires estimating the deformation", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "score": 1.0, + "content": "objectives with spatial discretization and maintaining vertex connectivity in a way that preserves", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 105, + 507, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 507, + 118 + ], + "score": 1.0, + "content": "topology [42]. We deform neural fields with a continuous invertible field to circumvent these issues.", + "type": "text", + "cross_page": true + } + ], + "index": 3 + } + ], + "index": 49.5, + "bbox_fs": [ + 104, + 677, + 506, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 73, + 505, + 117 + ], + "lines": [ + { + "bbox": [ + 106, + 73, + 504, + 84 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 504, + 84 + ], + "score": 1.0, + "content": "solvers [9]. Recent research also applies deep learning to optimize for non-linear deformation", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "score": 1.0, + "content": "losses [32, 34, 38, 80, 81, 83]. Deforming a mesh, however, requires estimating the deformation", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "score": 1.0, + "content": "objectives with spatial discretization and maintaining vertex connectivity in a way that preserves", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 105, + 507, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 507, + 118 + ], + "score": 1.0, + "content": "topology [42]. We deform neural fields with a continuous invertible field to circumvent these issues.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "text", + "bbox": [ + 106, + 129, + 505, + 294 + ], + "lines": [ + { + "bbox": [ + 105, + 128, + 505, + 142 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 505, + 142 + ], + "score": 1.0, + "content": "Implicit field deformation. Prior works have studied the deformation of implicit fields for tasks", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 140, + 505, + 153 + ], + "spans": [ + { + "bbox": [ + 105, + 140, + 505, + 153 + ], + "score": 1.0, + "content": "like physics simulation [39, 51, 54, 55]. These works use voxels or octrees to represent implicit", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 150, + 506, + 165 + ], + "spans": [ + { + "bbox": [ + 105, + 150, + 506, + 165 + ], + "score": 1.0, + "content": "fields, while our paper advocates for using neural fields for deformation. There is some past work on", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 162, + 505, + 176 + ], + "spans": [ + { + "bbox": [ + 105, + 162, + 505, + 176 + ], + "score": 1.0, + "content": "deforming neural fields to match a target shape [12, 18, 37, 53, 58] or image [43, 57, 60] without any", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 173, + 506, + 186 + ], + "spans": [ + { + "bbox": [ + 105, + 173, + 506, + 186 + ], + "score": 1.0, + "content": "correspondences between the two. In contrast, we perform such deformation with very few localized", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 183, + 506, + 198 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 506, + 198 + ], + "score": 1.0, + "content": "user-provided correspondences, but without any other information about the target shape. Our setting", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 195, + 506, + 208 + ], + "spans": [ + { + "bbox": [ + 105, + 195, + 506, + 208 + ], + "score": 1.0, + "content": "is very convenient for artists, but it requires the algorithm to provide a strong surface prior due to", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 205, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 505, + 218 + ], + "score": 1.0, + "content": "the lack of a densely specified target state. Other prior works on editing neural fields are trained on", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 216, + 506, + 230 + ], + "spans": [ + { + "bbox": [ + 104, + 216, + 506, + 230 + ], + "score": 1.0, + "content": "a dataset of shapes from a particular object category [25, 29, 30, 33, 85]. Since surface priors are", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 228, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 106, + 228, + 506, + 241 + ], + "score": 1.0, + "content": "specified implicitly by the dataset, it is unclear how to apply these methods to out-of-distribution", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 239, + 505, + 251 + ], + "spans": [ + { + "bbox": [ + 106, + 239, + 505, + 251 + ], + "score": 1.0, + "content": "shapes. In contrast, our paper requires no training dataset and instead enforces priors inspired by", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 249, + 505, + 262 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 505, + 262 + ], + "score": 1.0, + "content": "more general physical properties such as smoothness and elasticity. Remelli et al. [62] developed", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 261, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 261, + 505, + 273 + ], + "score": 1.0, + "content": "a way to differentiate iso-surface extraction, which allows deforming neural fields using objectives", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 271, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 106, + 271, + 505, + 284 + ], + "score": 1.0, + "content": "carried over from mesh-based algorithms. Our method avoids iso-surface extraction entirely and", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 282, + 417, + 295 + ], + "spans": [ + { + "bbox": [ + 106, + 282, + 417, + 295 + ], + "score": 1.0, + "content": "formulates differentiable deformation objectives directly on the implicit field.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 11 + }, + { + "type": "title", + "bbox": [ + 107, + 310, + 367, + 324 + ], + "lines": [ + { + "bbox": [ + 104, + 309, + 369, + 327 + ], + "spans": [ + { + "bbox": [ + 104, + 309, + 369, + 327 + ], + "score": 1.0, + "content": "3 Computing Surface Properties of Neural Fields", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 335, + 505, + 413 + ], + "lines": [ + { + "bbox": [ + 105, + 335, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 505, + 349 + ], + "score": 1.0, + "content": "In this section, we will discuss how to compute surface properties using neural fields and establish", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 346, + 506, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 267, + 359 + ], + "score": 1.0, + "content": "notation for the following sections. Let", + "type": "text" + }, + { + "bbox": [ + 267, + 347, + 281, + 357 + ], + "score": 0.75, + "content": "\\partial \\Omega", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 346, + 417, + 359 + ], + "score": 1.0, + "content": "be a surface enclosing the region", + "type": "text" + }, + { + "bbox": [ + 418, + 347, + 426, + 357 + ], + "score": 0.76, + "content": "\\Omega", + "type": "inline_equation" + }, + { + "bbox": [ + 426, + 346, + 506, + 359 + ], + "score": 1.0, + "content": ". A signed distance", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 356, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 104, + 356, + 203, + 371 + ], + "score": 1.0, + "content": "field (SDF) for surface", + "type": "text" + }, + { + "bbox": [ + 203, + 358, + 218, + 368 + ], + "score": 0.83, + "content": "\\partial \\Omega", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 356, + 273, + 371 + ], + "score": 1.0, + "content": "is defined as", + "type": "text" + }, + { + "bbox": [ + 274, + 357, + 403, + 370 + ], + "score": 0.92, + "content": "d ( \\mathbf { x } ) = s ( \\mathbf { x } ) \\operatorname* { m i n } _ { \\mathbf { y } \\in \\partial \\Omega } \\bar { \\| } \\mathbf { x } - \\mathbf { y } \\bar { \\| }", + "type": "inline_equation" + }, + { + "bbox": [ + 403, + 356, + 485, + 371 + ], + "score": 1.0, + "content": ". The sign function", + "type": "text" + }, + { + "bbox": [ + 485, + 357, + 505, + 370 + ], + "score": 0.91, + "content": "s ( \\mathbf { x } )", + "type": "inline_equation" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 158, + 381 + ], + "score": 1.0, + "content": "evaluates to", + "type": "text" + }, + { + "bbox": [ + 159, + 369, + 173, + 379 + ], + "score": 0.7, + "content": "- 1", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 368, + 184, + 381 + ], + "score": 1.0, + "content": "if", + "type": "text" + }, + { + "bbox": [ + 184, + 369, + 215, + 379 + ], + "score": 0.9, + "content": "\\textbf { x } \\in { \\Omega }", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "and 1 otherwise. We will assume that a neural field approximate an", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 379, + 504, + 391 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 436, + 390 + ], + "score": 1.0, + "content": "SDF whose zero-isosurface represents the surface of interest. For a neural field", + "type": "text" + }, + { + "bbox": [ + 436, + 380, + 443, + 391 + ], + "score": 0.84, + "content": "f", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 379, + 504, + 390 + ], + "score": 1.0, + "content": ", we denote its", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 391, + 192, + 402 + ], + "score": 1.0, + "content": "zero-isosurface using", + "type": "text" + }, + { + "bbox": [ + 193, + 390, + 211, + 403 + ], + "score": 0.9, + "content": "\\mathcal { M } _ { f }", + "type": "inline_equation" + }, + { + "bbox": [ + 211, + 391, + 505, + 402 + ], + "score": 1.0, + "content": ". This section summarizes how to compute surface normals and curvatures", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 401, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 506, + 414 + ], + "score": 1.0, + "content": "from neural fields. This is well-understood and we summarize this here for convenience [39, 54, 59].", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 107, + 425, + 505, + 536 + ], + "lines": [ + { + "bbox": [ + 105, + 424, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 505, + 438 + ], + "score": 1.0, + "content": "Surface normal. The surface normal is the vector perpendicular to the tangent plane and describes", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 437, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 106, + 437, + 505, + 448 + ], + "score": 1.0, + "content": "the local orientation of the surface. For an SDF, the outward oriented surface normal of its level set is", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 447, + 506, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 181, + 460 + ], + "score": 1.0, + "content": "the field gradient:", + "type": "text" + }, + { + "bbox": [ + 182, + 447, + 254, + 460 + ], + "score": 0.92, + "content": "\\mathbf { n } _ { d } ( \\mathbf { x } ) = \\nabla _ { \\mathbf { x } } d ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 447, + 506, + 460 + ], + "score": 1.0, + "content": ". It can be shown that the SDF’s gradient norm is always one:", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 107, + 458, + 506, + 471 + ], + "spans": [ + { + "bbox": [ + 107, + 458, + 168, + 470 + ], + "score": 0.92, + "content": "\\lVert \\nabla _ { \\mathbf { x } } d ( \\mathbf { x } ) \\rVert = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 169, + 458, + 506, + 471 + ], + "score": 1.0, + "content": ". This property can be used to ensure that the field remains a valid SDF throughout", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 104, + 468, + 506, + 482 + ], + "spans": [ + { + "bbox": [ + 104, + 468, + 298, + 482 + ], + "score": 1.0, + "content": "any manipulation [4, 31]. The closest point in", + "type": "text" + }, + { + "bbox": [ + 298, + 469, + 313, + 479 + ], + "score": 0.71, + "content": "\\partial \\Omega", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 468, + 336, + 482 + ], + "score": 1.0, + "content": "from", + "type": "text" + }, + { + "bbox": [ + 336, + 471, + 345, + 479 + ], + "score": 0.46, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 345, + 468, + 415, + 482 + ], + "score": 1.0, + "content": "can be found by", + "type": "text" + }, + { + "bbox": [ + 415, + 469, + 479, + 481 + ], + "score": 0.93, + "content": "\\mathbf { x } - d ( \\mathbf { x } ) \\mathbf { n } _ { d } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 479, + 468, + 506, + 482 + ], + "score": 1.0, + "content": ". This", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 479, + 506, + 493 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 506, + 493 + ], + "score": 1.0, + "content": "property can be used to sample points from the isosurface without creating a mesh [5, 13]. Finally,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 492, + 505, + 503 + ], + "spans": [ + { + "bbox": [ + 106, + 492, + 505, + 503 + ], + "score": 1.0, + "content": "since the tangent plane is perpendicular to the surface normal, we can project vectors onto the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 502, + 506, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 502, + 495, + 515 + ], + "score": 1.0, + "content": "tangent plane by subtracting their projection onto the normal using the following projection matrix", + "type": "text" + }, + { + "bbox": [ + 495, + 504, + 502, + 512 + ], + "score": 0.26, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 502, + 506, + 515 + ], + "score": 1.0, + "content": ":", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 512, + 506, + 526 + ], + "spans": [ + { + "bbox": [ + 106, + 512, + 219, + 525 + ], + "score": 0.92, + "content": "\\mathbf { P } _ { d } \\mathbf { \\bar { ( x ) } } \\overset { \\mathbf { \\bar { \\alpha } } } { = } \\mathbf { I } - \\mathbf { \\bar { n _ { d } } } \\mathbf { ( x ) } \\mathbf { n } _ { d } \\mathbf { ( x ) } \\mathbf { \\breve { \\alpha } }", + "type": "inline_equation" + }, + { + "bbox": [ + 220, + 512, + 506, + 526 + ], + "score": 1.0, + "content": ". This projection matrix allows us to characterize the tangent plane. This", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 524, + 507, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 524, + 507, + 537 + ], + "score": 1.0, + "content": "matrix is important for measuring how much a given deformation stretches the tangent direction [35].", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 31.5 + }, + { + "type": "text", + "bbox": [ + 107, + 548, + 505, + 625 + ], + "lines": [ + { + "bbox": [ + 106, + 548, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 548, + 505, + 561 + ], + "score": 1.0, + "content": "Curvature. Intuitively, curvature describes how much a surface deviates from a plane. This can", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "score": 1.0, + "content": "be captured by the total derivative of the surface normal, which is also known as the shape operator:", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 107, + 569, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 107, + 570, + 181, + 582 + ], + "score": 0.92, + "content": "\\bar { \\mathbf { \\xi } } S _ { D } ( \\bar { \\mathbf { x } } ) = \\mathcal { D } \\bar { \\mathbf { n } _ { d } } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 569, + 505, + 583 + ], + "score": 1.0, + "content": ". For an SDF, the normal itself is given by the derivative of the field, thus the shape", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 104, + 580, + 506, + 594 + ], + "spans": [ + { + "bbox": [ + 104, + 580, + 333, + 594 + ], + "score": 1.0, + "content": "operator for an SDF is the Hessian of the field function:", + "type": "text" + }, + { + "bbox": [ + 333, + 580, + 405, + 593 + ], + "score": 0.93, + "content": "\\dot { H _ { d } } ( \\mathbf { x } ) = \\mathcal { D } ^ { 2 } d ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 580, + 506, + 594 + ], + "score": 1.0, + "content": ". The shape operator can", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 592, + 506, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 506, + 604 + ], + "score": 1.0, + "content": "be used to capture many different notions of curvature, including mean curvature (half the trace of", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 107, + 602, + 505, + 615 + ], + "spans": [ + { + "bbox": [ + 107, + 603, + 135, + 615 + ], + "score": 0.92, + "content": "S _ { D } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 602, + 184, + 615 + ], + "score": 1.0, + "content": ", denoted by", + "type": "text" + }, + { + "bbox": [ + 185, + 604, + 191, + 613 + ], + "score": 0.73, + "content": "\\bar { \\kappa }", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 602, + 354, + 615 + ], + "score": 1.0, + "content": "), Gaussian curvature (the determinant of", + "type": "text" + }, + { + "bbox": [ + 354, + 603, + 384, + 614 + ], + "score": 0.91, + "content": "S _ { D } ( { \\bf x } ) _ { , }", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 602, + 505, + 615 + ], + "score": 1.0, + "content": "), and principal curvatures (the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 613, + 497, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 166, + 626 + ], + "score": 1.0, + "content": "eigenvalues of", + "type": "text" + }, + { + "bbox": [ + 166, + 614, + 195, + 626 + ], + "score": 0.91, + "content": "S _ { D } ( { \\bf x } ) _ { , }", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 613, + 497, + 626 + ], + "score": 1.0, + "content": "). We will use these to define objectives that smooth or sharpen the surface.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 40 + }, + { + "type": "title", + "bbox": [ + 107, + 641, + 300, + 655 + ], + "lines": [ + { + "bbox": [ + 104, + 639, + 301, + 659 + ], + "spans": [ + { + "bbox": [ + 104, + 639, + 301, + 659 + ], + "score": 1.0, + "content": "4 Shape Smoothing and Sharpening", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 107, + 667, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "In this section, we will show that shape smoothing and sharpening can be done directly on neural", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "score": 1.0, + "content": "fields without producing meshes. In our setup, the input shape is represented as the zero-isosurface", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 107, + 686, + 503, + 703 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 126, + 700 + ], + "score": 0.91, + "content": "\\mathcal { M } _ { F }", + "type": "inline_equation" + }, + { + "bbox": [ + 127, + 686, + 198, + 703 + ], + "score": 1.0, + "content": "of the neural field", + "type": "text" + }, + { + "bbox": [ + 198, + 689, + 207, + 699 + ], + "score": 0.82, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 207, + 686, + 376, + 703 + ], + "score": 1.0, + "content": ". The algorithm needs to output neural field", + "type": "text" + }, + { + "bbox": [ + 376, + 689, + 389, + 700 + ], + "score": 0.9, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 390, + 686, + 480, + 703 + ], + "score": 1.0, + "content": "whose zero-isosurface", + "type": "text" + }, + { + "bbox": [ + 480, + 689, + 503, + 701 + ], + "score": 0.9, + "content": "\\mathcal { M } _ { G _ { \\theta } }", + "type": "inline_equation" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 212, + 713 + ], + "score": 1.0, + "content": "satisfies two goals. First,", + "type": "text" + }, + { + "bbox": [ + 212, + 700, + 235, + 712 + ], + "score": 0.91, + "content": "\\mathcal { M } _ { G _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 699, + 397, + 713 + ], + "score": 1.0, + "content": "should preserve the global structure of", + "type": "text" + }, + { + "bbox": [ + 398, + 700, + 417, + 711 + ], + "score": 0.9, + "content": "\\mathcal { M } _ { F }", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 699, + 505, + 713 + ], + "score": 1.0, + "content": ". Second, the surface", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 107, + 711, + 402, + 723 + ], + "spans": [ + { + "bbox": [ + 107, + 711, + 130, + 723 + ], + "score": 0.91, + "content": "\\mathcal { M } _ { G _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 130, + 711, + 378, + 723 + ], + "score": 1.0, + "content": "should make desired changes to match the curvature of shape", + "type": "text" + }, + { + "bbox": [ + 379, + 711, + 398, + 722 + ], + "score": 0.89, + "content": "\\mathcal { M } _ { F }", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 711, + 402, + 723 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 47 + } + ], + "page_idx": 2, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 741, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 740, + 309, + 752 + ], + "spans": [ + { + "bbox": [ + 301, + 740, + 309, + 752 + ], + "score": 1.0, + "content": "3", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 73, + 505, + 117 + ], + "lines": [], + "index": 1.5, + "bbox_fs": [ + 105, + 73, + 507, + 118 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 129, + 505, + 294 + ], + "lines": [ + { + "bbox": [ + 105, + 128, + 505, + 142 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 505, + 142 + ], + "score": 1.0, + "content": "Implicit field deformation. Prior works have studied the deformation of implicit fields for tasks", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 140, + 505, + 153 + ], + "spans": [ + { + "bbox": [ + 105, + 140, + 505, + 153 + ], + "score": 1.0, + "content": "like physics simulation [39, 51, 54, 55]. These works use voxels or octrees to represent implicit", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 150, + 506, + 165 + ], + "spans": [ + { + "bbox": [ + 105, + 150, + 506, + 165 + ], + "score": 1.0, + "content": "fields, while our paper advocates for using neural fields for deformation. There is some past work on", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 162, + 505, + 176 + ], + "spans": [ + { + "bbox": [ + 105, + 162, + 505, + 176 + ], + "score": 1.0, + "content": "deforming neural fields to match a target shape [12, 18, 37, 53, 58] or image [43, 57, 60] without any", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 173, + 506, + 186 + ], + "spans": [ + { + "bbox": [ + 105, + 173, + 506, + 186 + ], + "score": 1.0, + "content": "correspondences between the two. In contrast, we perform such deformation with very few localized", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 183, + 506, + 198 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 506, + 198 + ], + "score": 1.0, + "content": "user-provided correspondences, but without any other information about the target shape. Our setting", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 195, + 506, + 208 + ], + "spans": [ + { + "bbox": [ + 105, + 195, + 506, + 208 + ], + "score": 1.0, + "content": "is very convenient for artists, but it requires the algorithm to provide a strong surface prior due to", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 205, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 505, + 218 + ], + "score": 1.0, + "content": "the lack of a densely specified target state. Other prior works on editing neural fields are trained on", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 216, + 506, + 230 + ], + "spans": [ + { + "bbox": [ + 104, + 216, + 506, + 230 + ], + "score": 1.0, + "content": "a dataset of shapes from a particular object category [25, 29, 30, 33, 85]. Since surface priors are", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 228, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 106, + 228, + 506, + 241 + ], + "score": 1.0, + "content": "specified implicitly by the dataset, it is unclear how to apply these methods to out-of-distribution", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 239, + 505, + 251 + ], + "spans": [ + { + "bbox": [ + 106, + 239, + 505, + 251 + ], + "score": 1.0, + "content": "shapes. In contrast, our paper requires no training dataset and instead enforces priors inspired by", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 249, + 505, + 262 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 505, + 262 + ], + "score": 1.0, + "content": "more general physical properties such as smoothness and elasticity. Remelli et al. [62] developed", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 261, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 261, + 505, + 273 + ], + "score": 1.0, + "content": "a way to differentiate iso-surface extraction, which allows deforming neural fields using objectives", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 271, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 106, + 271, + 505, + 284 + ], + "score": 1.0, + "content": "carried over from mesh-based algorithms. Our method avoids iso-surface extraction entirely and", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 282, + 417, + 295 + ], + "spans": [ + { + "bbox": [ + 106, + 282, + 417, + 295 + ], + "score": 1.0, + "content": "formulates differentiable deformation objectives directly on the implicit field.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 11, + "bbox_fs": [ + 104, + 128, + 506, + 295 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 310, + 367, + 324 + ], + "lines": [ + { + "bbox": [ + 104, + 309, + 369, + 327 + ], + "spans": [ + { + "bbox": [ + 104, + 309, + 369, + 327 + ], + "score": 1.0, + "content": "3 Computing Surface Properties of Neural Fields", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 335, + 505, + 413 + ], + "lines": [ + { + "bbox": [ + 105, + 335, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 505, + 349 + ], + "score": 1.0, + "content": "In this section, we will discuss how to compute surface properties using neural fields and establish", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 346, + 506, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 267, + 359 + ], + "score": 1.0, + "content": "notation for the following sections. Let", + "type": "text" + }, + { + "bbox": [ + 267, + 347, + 281, + 357 + ], + "score": 0.75, + "content": "\\partial \\Omega", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 346, + 417, + 359 + ], + "score": 1.0, + "content": "be a surface enclosing the region", + "type": "text" + }, + { + "bbox": [ + 418, + 347, + 426, + 357 + ], + "score": 0.76, + "content": "\\Omega", + "type": "inline_equation" + }, + { + "bbox": [ + 426, + 346, + 506, + 359 + ], + "score": 1.0, + "content": ". A signed distance", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 356, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 104, + 356, + 203, + 371 + ], + "score": 1.0, + "content": "field (SDF) for surface", + "type": "text" + }, + { + "bbox": [ + 203, + 358, + 218, + 368 + ], + "score": 0.83, + "content": "\\partial \\Omega", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 356, + 273, + 371 + ], + "score": 1.0, + "content": "is defined as", + "type": "text" + }, + { + "bbox": [ + 274, + 357, + 403, + 370 + ], + "score": 0.92, + "content": "d ( \\mathbf { x } ) = s ( \\mathbf { x } ) \\operatorname* { m i n } _ { \\mathbf { y } \\in \\partial \\Omega } \\bar { \\| } \\mathbf { x } - \\mathbf { y } \\bar { \\| }", + "type": "inline_equation" + }, + { + "bbox": [ + 403, + 356, + 485, + 371 + ], + "score": 1.0, + "content": ". The sign function", + "type": "text" + }, + { + "bbox": [ + 485, + 357, + 505, + 370 + ], + "score": 0.91, + "content": "s ( \\mathbf { x } )", + "type": "inline_equation" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 158, + 381 + ], + "score": 1.0, + "content": "evaluates to", + "type": "text" + }, + { + "bbox": [ + 159, + 369, + 173, + 379 + ], + "score": 0.7, + "content": "- 1", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 368, + 184, + 381 + ], + "score": 1.0, + "content": "if", + "type": "text" + }, + { + "bbox": [ + 184, + 369, + 215, + 379 + ], + "score": 0.9, + "content": "\\textbf { x } \\in { \\Omega }", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "and 1 otherwise. We will assume that a neural field approximate an", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 379, + 504, + 391 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 436, + 390 + ], + "score": 1.0, + "content": "SDF whose zero-isosurface represents the surface of interest. For a neural field", + "type": "text" + }, + { + "bbox": [ + 436, + 380, + 443, + 391 + ], + "score": 0.84, + "content": "f", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 379, + 504, + 390 + ], + "score": 1.0, + "content": ", we denote its", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 391, + 192, + 402 + ], + "score": 1.0, + "content": "zero-isosurface using", + "type": "text" + }, + { + "bbox": [ + 193, + 390, + 211, + 403 + ], + "score": 0.9, + "content": "\\mathcal { M } _ { f }", + "type": "inline_equation" + }, + { + "bbox": [ + 211, + 391, + 505, + 402 + ], + "score": 1.0, + "content": ". This section summarizes how to compute surface normals and curvatures", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 401, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 506, + 414 + ], + "score": 1.0, + "content": "from neural fields. This is well-understood and we summarize this here for convenience [39, 54, 59].", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 23, + "bbox_fs": [ + 104, + 335, + 506, + 414 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 425, + 505, + 536 + ], + "lines": [ + { + "bbox": [ + 105, + 424, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 505, + 438 + ], + "score": 1.0, + "content": "Surface normal. The surface normal is the vector perpendicular to the tangent plane and describes", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 437, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 106, + 437, + 505, + 448 + ], + "score": 1.0, + "content": "the local orientation of the surface. For an SDF, the outward oriented surface normal of its level set is", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 447, + 506, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 181, + 460 + ], + "score": 1.0, + "content": "the field gradient:", + "type": "text" + }, + { + "bbox": [ + 182, + 447, + 254, + 460 + ], + "score": 0.92, + "content": "\\mathbf { n } _ { d } ( \\mathbf { x } ) = \\nabla _ { \\mathbf { x } } d ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 447, + 506, + 460 + ], + "score": 1.0, + "content": ". It can be shown that the SDF’s gradient norm is always one:", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 107, + 458, + 506, + 471 + ], + "spans": [ + { + "bbox": [ + 107, + 458, + 168, + 470 + ], + "score": 0.92, + "content": "\\lVert \\nabla _ { \\mathbf { x } } d ( \\mathbf { x } ) \\rVert = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 169, + 458, + 506, + 471 + ], + "score": 1.0, + "content": ". This property can be used to ensure that the field remains a valid SDF throughout", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 104, + 468, + 506, + 482 + ], + "spans": [ + { + "bbox": [ + 104, + 468, + 298, + 482 + ], + "score": 1.0, + "content": "any manipulation [4, 31]. The closest point in", + "type": "text" + }, + { + "bbox": [ + 298, + 469, + 313, + 479 + ], + "score": 0.71, + "content": "\\partial \\Omega", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 468, + 336, + 482 + ], + "score": 1.0, + "content": "from", + "type": "text" + }, + { + "bbox": [ + 336, + 471, + 345, + 479 + ], + "score": 0.46, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 345, + 468, + 415, + 482 + ], + "score": 1.0, + "content": "can be found by", + "type": "text" + }, + { + "bbox": [ + 415, + 469, + 479, + 481 + ], + "score": 0.93, + "content": "\\mathbf { x } - d ( \\mathbf { x } ) \\mathbf { n } _ { d } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 479, + 468, + 506, + 482 + ], + "score": 1.0, + "content": ". This", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 479, + 506, + 493 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 506, + 493 + ], + "score": 1.0, + "content": "property can be used to sample points from the isosurface without creating a mesh [5, 13]. Finally,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 492, + 505, + 503 + ], + "spans": [ + { + "bbox": [ + 106, + 492, + 505, + 503 + ], + "score": 1.0, + "content": "since the tangent plane is perpendicular to the surface normal, we can project vectors onto the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 502, + 506, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 502, + 495, + 515 + ], + "score": 1.0, + "content": "tangent plane by subtracting their projection onto the normal using the following projection matrix", + "type": "text" + }, + { + "bbox": [ + 495, + 504, + 502, + 512 + ], + "score": 0.26, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 502, + 506, + 515 + ], + "score": 1.0, + "content": ":", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 512, + 506, + 526 + ], + "spans": [ + { + "bbox": [ + 106, + 512, + 219, + 525 + ], + "score": 0.92, + "content": "\\mathbf { P } _ { d } \\mathbf { \\bar { ( x ) } } \\overset { \\mathbf { \\bar { \\alpha } } } { = } \\mathbf { I } - \\mathbf { \\bar { n _ { d } } } \\mathbf { ( x ) } \\mathbf { n } _ { d } \\mathbf { ( x ) } \\mathbf { \\breve { \\alpha } }", + "type": "inline_equation" + }, + { + "bbox": [ + 220, + 512, + 506, + 526 + ], + "score": 1.0, + "content": ". This projection matrix allows us to characterize the tangent plane. This", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 524, + 507, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 524, + 507, + 537 + ], + "score": 1.0, + "content": "matrix is important for measuring how much a given deformation stretches the tangent direction [35].", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 31.5, + "bbox_fs": [ + 104, + 424, + 507, + 537 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 548, + 505, + 625 + ], + "lines": [ + { + "bbox": [ + 106, + 548, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 548, + 505, + 561 + ], + "score": 1.0, + "content": "Curvature. Intuitively, curvature describes how much a surface deviates from a plane. This can", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "score": 1.0, + "content": "be captured by the total derivative of the surface normal, which is also known as the shape operator:", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 107, + 569, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 107, + 570, + 181, + 582 + ], + "score": 0.92, + "content": "\\bar { \\mathbf { \\xi } } S _ { D } ( \\bar { \\mathbf { x } } ) = \\mathcal { D } \\bar { \\mathbf { n } _ { d } } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 569, + 505, + 583 + ], + "score": 1.0, + "content": ". For an SDF, the normal itself is given by the derivative of the field, thus the shape", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 104, + 580, + 506, + 594 + ], + "spans": [ + { + "bbox": [ + 104, + 580, + 333, + 594 + ], + "score": 1.0, + "content": "operator for an SDF is the Hessian of the field function:", + "type": "text" + }, + { + "bbox": [ + 333, + 580, + 405, + 593 + ], + "score": 0.93, + "content": "\\dot { H _ { d } } ( \\mathbf { x } ) = \\mathcal { D } ^ { 2 } d ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 580, + 506, + 594 + ], + "score": 1.0, + "content": ". The shape operator can", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 592, + 506, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 506, + 604 + ], + "score": 1.0, + "content": "be used to capture many different notions of curvature, including mean curvature (half the trace of", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 107, + 602, + 505, + 615 + ], + "spans": [ + { + "bbox": [ + 107, + 603, + 135, + 615 + ], + "score": 0.92, + "content": "S _ { D } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 602, + 184, + 615 + ], + "score": 1.0, + "content": ", denoted by", + "type": "text" + }, + { + "bbox": [ + 185, + 604, + 191, + 613 + ], + "score": 0.73, + "content": "\\bar { \\kappa }", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 602, + 354, + 615 + ], + "score": 1.0, + "content": "), Gaussian curvature (the determinant of", + "type": "text" + }, + { + "bbox": [ + 354, + 603, + 384, + 614 + ], + "score": 0.91, + "content": "S _ { D } ( { \\bf x } ) _ { , }", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 602, + 505, + 615 + ], + "score": 1.0, + "content": "), and principal curvatures (the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 613, + 497, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 166, + 626 + ], + "score": 1.0, + "content": "eigenvalues of", + "type": "text" + }, + { + "bbox": [ + 166, + 614, + 195, + 626 + ], + "score": 0.91, + "content": "S _ { D } ( { \\bf x } ) _ { , }", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 613, + 497, + 626 + ], + "score": 1.0, + "content": "). We will use these to define objectives that smooth or sharpen the surface.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 40, + "bbox_fs": [ + 104, + 548, + 506, + 626 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 641, + 300, + 655 + ], + "lines": [ + { + "bbox": [ + 104, + 639, + 301, + 659 + ], + "spans": [ + { + "bbox": [ + 104, + 639, + 301, + 659 + ], + "score": 1.0, + "content": "4 Shape Smoothing and Sharpening", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 107, + 667, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "In this section, we will show that shape smoothing and sharpening can be done directly on neural", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "score": 1.0, + "content": "fields without producing meshes. In our setup, the input shape is represented as the zero-isosurface", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 107, + 686, + 503, + 703 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 126, + 700 + ], + "score": 0.91, + "content": "\\mathcal { M } _ { F }", + "type": "inline_equation" + }, + { + "bbox": [ + 127, + 686, + 198, + 703 + ], + "score": 1.0, + "content": "of the neural field", + "type": "text" + }, + { + "bbox": [ + 198, + 689, + 207, + 699 + ], + "score": 0.82, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 207, + 686, + 376, + 703 + ], + "score": 1.0, + "content": ". The algorithm needs to output neural field", + "type": "text" + }, + { + "bbox": [ + 376, + 689, + 389, + 700 + ], + "score": 0.9, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 390, + 686, + 480, + 703 + ], + "score": 1.0, + "content": "whose zero-isosurface", + "type": "text" + }, + { + "bbox": [ + 480, + 689, + 503, + 701 + ], + "score": 0.9, + "content": "\\mathcal { M } _ { G _ { \\theta } }", + "type": "inline_equation" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 212, + 713 + ], + "score": 1.0, + "content": "satisfies two goals. 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(A) zoomed-in input; (B) our method; (C) baseline", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 243, + 505, + 257 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 505, + 257 + ], + "score": 1.0, + "content": "without remeshing; (D) baseline with remeshing. We can see that the baseline without remeshing", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 255, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 106, + 255, + 505, + 267 + ], + "score": 1.0, + "content": "finds it difficult to smooth or sharpen the mesh extracted from neural fields. Our method is able to", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 267, + 320, + 278 + ], + "spans": [ + { + "bbox": [ + 106, + 267, + 320, + 278 + ], + "score": 1.0, + "content": "achieve good results without discretizing the surface.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 106, + 291, + 505, + 314 + ], + "lines": [ + { + "bbox": [ + 106, + 291, + 503, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 291, + 273, + 304 + ], + "score": 1.0, + "content": "To achieve these goals, we first instantiate", + "type": "text" + }, + { + "bbox": [ + 273, + 292, + 287, + 303 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 287, + 291, + 494, + 304 + ], + "score": 1.0, + "content": "using the same architecture and parameter values as", + "type": "text" + }, + { + "bbox": [ + 494, + 292, + 503, + 302 + ], + "score": 0.85, + "content": "F", + "type": "inline_equation" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 302, + 316, + 315 + ], + "spans": [ + { + "bbox": [ + 106, + 302, + 181, + 315 + ], + "score": 1.0, + "content": "Then we optimize", + "type": "text" + }, + { + "bbox": [ + 181, + 303, + 194, + 314 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 194, + 302, + 316, + 315 + ], + "score": 1.0, + "content": "using the following objective:", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5 + }, + { + "type": "interline_equation", + "bbox": [ + 110, + 322, + 498, + 357 + ], + "lines": [ + { + "bbox": [ + 110, + 322, + 498, + 357 + ], + "spans": [ + { + "bbox": [ + 110, + 322, + 498, + 357 + ], + "score": 0.92, + "content": "\\mathcal { L } ( \\theta ) = \\int _ { \\mathbf { x } \\in U } \\left| G _ { \\theta } ( \\mathbf { x } ) - F ( \\mathbf { x } ) \\right| ^ { 2 } + \\lambda _ { g } \\left( \\left\\| \\nabla _ { \\mathbf { x } } G _ { \\theta } ( \\mathbf { x } ) \\right\\| - 1 \\right) ^ { 2 } d \\mathbf { x } + \\int _ { \\mathbf { x } \\in V _ { \\tau } } \\lambda _ { k } \\left( \\kappa _ { G _ { \\theta } } ( \\mathbf { x } ) - \\beta \\kappa _ { F } ( \\mathbf { x } ) \\right) ^ { 2 } d \\mathbf { x } .", + "type": "interline_equation", + "image_path": "318f4b7b85ff34c65448f1858758db87fc47d86433ef6e6cdd2a92d8816934ea.jpg" + } + ] + } + ], + "index": 10, + "virtual_lines": [ + { + "bbox": [ + 110, + 322, + 498, + 333.6666666666667 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 110, + 333.6666666666667, + 498, + 345.33333333333337 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 110, + 345.33333333333337, + 498, + 357.00000000000006 + ], + "spans": [], + "index": 11 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 383, + 376, + 504 + ], + "lines": [ + { + "bbox": [ + 106, + 383, + 376, + 395 + ], + "spans": [ + { + "bbox": [ + 106, + 383, + 269, + 395 + ], + "score": 1.0, + "content": "The first integral encourages the network", + "type": "text" + }, + { + "bbox": [ + 269, + 384, + 282, + 394 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 383, + 376, + 395 + ], + "score": 1.0, + "content": "to preserve the original", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 393, + 377, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 262, + 406 + ], + "score": 1.0, + "content": "shape. The second term regularizes", + "type": "text" + }, + { + "bbox": [ + 262, + 395, + 276, + 405 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 276, + 393, + 377, + 406 + ], + "score": 1.0, + "content": "to remain a valid SDF", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 405, + 376, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 376, + 417 + ], + "score": 1.0, + "content": "by enforcing that the norm of the gradient is 1 (i.e., the Eikonal", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 416, + 376, + 428 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 337, + 428 + ], + "score": 1.0, + "content": "constraint [4, 31]). The integration is over the region", + "type": "text" + }, + { + "bbox": [ + 337, + 416, + 347, + 426 + ], + "score": 0.77, + "content": "U", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 416, + 376, + 428 + ], + "score": 1.0, + "content": "where", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 426, + 376, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 204, + 438 + ], + "score": 1.0, + "content": "the original neural field", + "type": "text" + }, + { + "bbox": [ + 205, + 427, + 214, + 437 + ], + "score": 0.82, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 426, + 376, + 438 + ], + "score": 1.0, + "content": "is supervised over. The final term aims", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 438, + 376, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 376, + 450 + ], + "score": 1.0, + "content": "to smooth or sharpen the surface by increasing or decreasing the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 449, + 377, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 146, + 460 + ], + "score": 1.0, + "content": "curvature", + "type": "text" + }, + { + "bbox": [ + 146, + 451, + 153, + 459 + ], + "score": 0.63, + "content": "\\kappa", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 449, + 187, + 460 + ], + "score": 1.0, + "content": ". Setting", + "type": "text" + }, + { + "bbox": [ + 188, + 449, + 213, + 460 + ], + "score": 0.91, + "content": "\\beta < 1", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 449, + 377, + 460 + ], + "score": 1.0, + "content": "will decrease the curvature of the output", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 459, + 377, + 472 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 139, + 472 + ], + "score": 1.0, + "content": "surface", + "type": "text" + }, + { + "bbox": [ + 139, + 461, + 156, + 471 + ], + "score": 0.89, + "content": "\\kappa _ { G _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 156, + 459, + 294, + 472 + ], + "score": 1.0, + "content": ", resulting in a smoother shape.", + "type": "text" + }, + { + "bbox": [ + 294, + 460, + 324, + 471 + ], + "score": 0.91, + "content": "\\beta > 1", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 459, + 377, + 472 + ], + "score": 1.0, + "content": "will lead to", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 469, + 378, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 378, + 483 + ], + "score": 1.0, + "content": "surfaces with higher curvature details and will thus sharpen shapes.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 481, + 376, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 376, + 494 + ], + "score": 1.0, + "content": "In this paper, we will use mean curvature since it’s easy to compute", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 491, + 275, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 181, + 505 + ], + "score": 1.0, + "content": "with neural fields:", + "type": "text" + }, + { + "bbox": [ + 181, + 492, + 270, + 505 + ], + "score": 0.93, + "content": "\\kappa _ { f } ( \\mathbf { x } ) = \\mathrm { t r } \\mathcal { D } ( \\mathbf { n } _ { f } ( \\mathbf { x } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 491, + 275, + 505 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 384, + 386, + 503, + 461 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 384, + 386, + 503, + 461 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 384, + 386, + 503, + 461 + ], + "spans": [ + { + "bbox": [ + 384, + 386, + 503, + 461 + ], + "score": 0.957, + "type": "image", + "image_path": "f46db6fa8fd3ad41d2bd57bfbf0b5032fd160bdb630f47e8f74bab8da49662dd.jpg" + } + ] + } + ], + "index": 23.5, + "virtual_lines": [ + { + "bbox": [ + 384, + 386, + 503, + 423.5 + ], + "spans": [], + "index": 23 + }, + { + "bbox": [ + 384, + 423.5, + 503, + 461.0 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 383, + 468, + 505, + 502 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 383, + 468, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 383, + 468, + 505, + 479 + ], + "score": 1.0, + "content": "Figure 1: L: SIREN learned", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 383, + 478, + 506, + 491 + ], + "spans": [ + { + "bbox": [ + 383, + 478, + 506, + 491 + ], + "score": 1.0, + "content": "to fit the SDF of a square; R:", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 383, + 491, + 494, + 502 + ], + "spans": [ + { + "bbox": [ + 383, + 491, + 494, + 502 + ], + "score": 1.0, + "content": "Zooming in on the surface.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26 + } + ], + "index": 24.75 + }, + { + "type": "text", + "bbox": [ + 106, + 509, + 505, + 586 + ], + "lines": [ + { + "bbox": [ + 106, + 508, + 505, + 521 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 505, + 521 + ], + "score": 1.0, + "content": "One challenge is that the computation of curvature can be very noisy for neural fields using periodic", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 519, + 506, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 506, + 532 + ], + "score": 1.0, + "content": "activations. Figure 4 shows how an ostensibly smooth isosurface learned through SIREN [66] is", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 531, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 531, + 505, + 543 + ], + "score": 1.0, + "content": "actually quite rough when zoomed in. The curvature evaluated on such a rough surface can be too", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "score": 1.0, + "content": "noisy to be used for training. To alleviate this issue, we only compute the curvature regularization in", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 552, + 505, + 564 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 394, + 564 + ], + "score": 1.0, + "content": "areas where the curvature of the level set is less than a certain threshold", + "type": "text" + }, + { + "bbox": [ + 395, + 554, + 402, + 562 + ], + "score": 0.69, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 552, + 505, + 564 + ], + "score": 1.0, + "content": ". Formally, we define this", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 563, + 504, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 136, + 577 + ], + "score": 1.0, + "content": "area as", + "type": "text" + }, + { + "bbox": [ + 137, + 563, + 292, + 576 + ], + "score": 0.91, + "content": "V _ { \\tau } = \\{ \\mathbf { x } \\in U | \\operatorname* { m a x } ( | \\kappa _ { G _ { \\theta } } | , | \\kappa _ { F } | ) < \\tau \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 292, + 563, + 492, + 577 + ], + "score": 1.0, + "content": ". We use rejection sampling to sample points from", + "type": "text" + }, + { + "bbox": [ + 492, + 563, + 504, + 574 + ], + "score": 0.84, + "content": "V _ { \\tau }", + "type": "inline_equation" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 574, + 272, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 272, + 587 + ], + "score": 1.0, + "content": "when computing the loss during training.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 106, + 601, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 601, + 506, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 601, + 506, + 614 + ], + "score": 1.0, + "content": "Results. We follow prior works [20, 76] to use Armadillo [40] and a sphere with one half of it", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 613, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 505, + 624 + ], + "score": 1.0, + "content": "corrupted by Gaussian noise. We compare our algorithm to two baselines. The first baseline directly", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 623, + 506, + 636 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 506, + 636 + ], + "score": 1.0, + "content": "applies the smoothing algorithm developed by Taubin [76] to the mesh extracted from the neural field", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 634, + 506, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 506, + 647 + ], + "score": 1.0, + "content": "using Marching cube [44]. The second baseline applies the filtering algorithms on meshes simplified", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 644, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 658 + ], + "score": 1.0, + "content": "by quadratic decimation [27]. The input neural fields are created following the procedure of Park", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "score": 1.0, + "content": "et al. [56]. The results are shown in Figure 2. The first baseline fails to smooth or sharpen the surface", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 667, + 506, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 506, + 680 + ], + "score": 1.0, + "content": "appropriately. It only modifies the surface with high-frequency noise. While the second baseline can", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 678, + 504, + 690 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 504, + 690 + ], + "score": 1.0, + "content": "filter the surface correctly, it introduces discretization artifacts due to the decimation process. This", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "suggests it is challenging to filter the neural field surface with mesh processing algorithms since these", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 700, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 700, + 505, + 712 + ], + "score": 1.0, + "content": "algorithms are sensitive to the quality of surface discretization. On the other hand, our algorithm can", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 711, + 488, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 488, + 723 + ], + "score": 1.0, + "content": "produce good filtering results without the need to maintain a good discretization of the surface.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 40 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 742, + 308, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 741, + 310, + 752 + ], + "spans": [ + { + "bbox": [ + 301, + 741, + 310, + 752 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 11, + "width": 9 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 70, + 504, + 230 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 109, + 70, + 504, + 230 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 70, + 504, + 230 + ], + "spans": [ + { + "bbox": [ + 109, + 70, + 504, + 230 + ], + "score": 0.97, + "type": "image", + "image_path": "a582fb6a973a707da2ca642467983ef490d9b46ef69834159125364e1493a4b2.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 109, + 70, + 504, + 123.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 109, + 123.33333333333334, + 504, + 176.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 109, + 176.66666666666669, + 504, + 230.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 233, + 505, + 277 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 232, + 505, + 245 + ], + "spans": [ + { + "bbox": [ + 106, + 232, + 505, + 245 + ], + "score": 1.0, + "content": "Figure 2: Smoothing and sharpening results. (A) zoomed-in input; (B) our method; (C) baseline", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 243, + 505, + 257 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 505, + 257 + ], + "score": 1.0, + "content": "without remeshing; (D) baseline with remeshing. We can see that the baseline without remeshing", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 255, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 106, + 255, + 505, + 267 + ], + "score": 1.0, + "content": "finds it difficult to smooth or sharpen the mesh extracted from neural fields. Our method is able to", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 267, + 320, + 278 + ], + "spans": [ + { + "bbox": [ + 106, + 267, + 320, + 278 + ], + "score": 1.0, + "content": "achieve good results without discretizing the surface.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 106, + 291, + 505, + 314 + ], + "lines": [ + { + "bbox": [ + 106, + 291, + 503, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 291, + 273, + 304 + ], + "score": 1.0, + "content": "To achieve these goals, we first instantiate", + "type": "text" + }, + { + "bbox": [ + 273, + 292, + 287, + 303 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 287, + 291, + 494, + 304 + ], + "score": 1.0, + "content": "using the same architecture and parameter values as", + "type": "text" + }, + { + "bbox": [ + 494, + 292, + 503, + 302 + ], + "score": 0.85, + "content": "F", + "type": "inline_equation" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 302, + 316, + 315 + ], + "spans": [ + { + "bbox": [ + 106, + 302, + 181, + 315 + ], + "score": 1.0, + "content": "Then we optimize", + "type": "text" + }, + { + "bbox": [ + 181, + 303, + 194, + 314 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 194, + 302, + 316, + 315 + ], + "score": 1.0, + "content": "using the following objective:", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5, + "bbox_fs": [ + 106, + 291, + 503, + 315 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 110, + 322, + 498, + 357 + ], + "lines": [ + { + "bbox": [ + 110, + 322, + 498, + 357 + ], + "spans": [ + { + "bbox": [ + 110, + 322, + 498, + 357 + ], + "score": 0.92, + "content": "\\mathcal { L } ( \\theta ) = \\int _ { \\mathbf { x } \\in U } \\left| G _ { \\theta } ( \\mathbf { x } ) - F ( \\mathbf { x } ) \\right| ^ { 2 } + \\lambda _ { g } \\left( \\left\\| \\nabla _ { \\mathbf { x } } G _ { \\theta } ( \\mathbf { x } ) \\right\\| - 1 \\right) ^ { 2 } d \\mathbf { x } + \\int _ { \\mathbf { x } \\in V _ { \\tau } } \\lambda _ { k } \\left( \\kappa _ { G _ { \\theta } } ( \\mathbf { x } ) - \\beta \\kappa _ { F } ( \\mathbf { x } ) \\right) ^ { 2 } d \\mathbf { x } .", + "type": "interline_equation", + "image_path": "318f4b7b85ff34c65448f1858758db87fc47d86433ef6e6cdd2a92d8816934ea.jpg" + } + ] + } + ], + "index": 10, + "virtual_lines": [ + { + "bbox": [ + 110, + 322, + 498, + 333.6666666666667 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 110, + 333.6666666666667, + 498, + 345.33333333333337 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 110, + 345.33333333333337, + 498, + 357.00000000000006 + ], + "spans": [], + "index": 11 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 383, + 376, + 504 + ], + "lines": [ + { + "bbox": [ + 106, + 383, + 376, + 395 + ], + "spans": [ + { + "bbox": [ + 106, + 383, + 269, + 395 + ], + "score": 1.0, + "content": "The first integral encourages the network", + "type": "text" + }, + { + "bbox": [ + 269, + 384, + 282, + 394 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 383, + 376, + 395 + ], + "score": 1.0, + "content": "to preserve the original", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 393, + 377, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 262, + 406 + ], + "score": 1.0, + "content": "shape. The second term regularizes", + "type": "text" + }, + { + "bbox": [ + 262, + 395, + 276, + 405 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 276, + 393, + 377, + 406 + ], + "score": 1.0, + "content": "to remain a valid SDF", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 405, + 376, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 376, + 417 + ], + "score": 1.0, + "content": "by enforcing that the norm of the gradient is 1 (i.e., the Eikonal", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 416, + 376, + 428 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 337, + 428 + ], + "score": 1.0, + "content": "constraint [4, 31]). The integration is over the region", + "type": "text" + }, + { + "bbox": [ + 337, + 416, + 347, + 426 + ], + "score": 0.77, + "content": "U", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 416, + 376, + 428 + ], + "score": 1.0, + "content": "where", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 426, + 376, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 204, + 438 + ], + "score": 1.0, + "content": "the original neural field", + "type": "text" + }, + { + "bbox": [ + 205, + 427, + 214, + 437 + ], + "score": 0.82, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 426, + 376, + 438 + ], + "score": 1.0, + "content": "is supervised over. The final term aims", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 438, + 376, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 376, + 450 + ], + "score": 1.0, + "content": "to smooth or sharpen the surface by increasing or decreasing the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 449, + 377, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 146, + 460 + ], + "score": 1.0, + "content": "curvature", + "type": "text" + }, + { + "bbox": [ + 146, + 451, + 153, + 459 + ], + "score": 0.63, + "content": "\\kappa", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 449, + 187, + 460 + ], + "score": 1.0, + "content": ". Setting", + "type": "text" + }, + { + "bbox": [ + 188, + 449, + 213, + 460 + ], + "score": 0.91, + "content": "\\beta < 1", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 449, + 377, + 460 + ], + "score": 1.0, + "content": "will decrease the curvature of the output", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 459, + 377, + 472 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 139, + 472 + ], + "score": 1.0, + "content": "surface", + "type": "text" + }, + { + "bbox": [ + 139, + 461, + 156, + 471 + ], + "score": 0.89, + "content": "\\kappa _ { G _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 156, + 459, + 294, + 472 + ], + "score": 1.0, + "content": ", resulting in a smoother shape.", + "type": "text" + }, + { + "bbox": [ + 294, + 460, + 324, + 471 + ], + "score": 0.91, + "content": "\\beta > 1", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 459, + 377, + 472 + ], + "score": 1.0, + "content": "will lead to", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 469, + 378, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 378, + 483 + ], + "score": 1.0, + "content": "surfaces with higher curvature details and will thus sharpen shapes.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 481, + 376, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 376, + 494 + ], + "score": 1.0, + "content": "In this paper, we will use mean curvature since it’s easy to compute", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 491, + 275, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 181, + 505 + ], + "score": 1.0, + "content": "with neural fields:", + "type": "text" + }, + { + "bbox": [ + 181, + 492, + 270, + 505 + ], + "score": 0.93, + "content": "\\kappa _ { f } ( \\mathbf { x } ) = \\mathrm { t r } \\mathcal { D } ( \\mathbf { n } _ { f } ( \\mathbf { x } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 491, + 275, + 505 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 17, + "bbox_fs": [ + 105, + 383, + 378, + 505 + ] + }, + { + "type": "image", + "bbox": [ + 384, + 386, + 503, + 461 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 384, + 386, + 503, + 461 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 384, + 386, + 503, + 461 + ], + "spans": [ + { + "bbox": [ + 384, + 386, + 503, + 461 + ], + "score": 0.957, + "type": "image", + "image_path": "f46db6fa8fd3ad41d2bd57bfbf0b5032fd160bdb630f47e8f74bab8da49662dd.jpg" + } + ] + } + ], + "index": 23.5, + "virtual_lines": [ + { + "bbox": [ + 384, + 386, + 503, + 423.5 + ], + "spans": [], + "index": 23 + }, + { + "bbox": [ + 384, + 423.5, + 503, + 461.0 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 383, + 468, + 505, + 502 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 383, + 468, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 383, + 468, + 505, + 479 + ], + "score": 1.0, + "content": "Figure 1: L: SIREN learned", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 383, + 478, + 506, + 491 + ], + "spans": [ + { + "bbox": [ + 383, + 478, + 506, + 491 + ], + "score": 1.0, + "content": "to fit the SDF of a square; R:", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 383, + 491, + 494, + 502 + ], + "spans": [ + { + "bbox": [ + 383, + 491, + 494, + 502 + ], + "score": 1.0, + "content": "Zooming in on the surface.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26 + } + ], + "index": 24.75 + }, + { + "type": "text", + "bbox": [ + 106, + 509, + 505, + 586 + ], + "lines": [ + { + "bbox": [ + 106, + 508, + 505, + 521 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 505, + 521 + ], + "score": 1.0, + "content": "One challenge is that the computation of curvature can be very noisy for neural fields using periodic", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 519, + 506, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 506, + 532 + ], + "score": 1.0, + "content": "activations. Figure 4 shows how an ostensibly smooth isosurface learned through SIREN [66] is", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 531, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 531, + 505, + 543 + ], + "score": 1.0, + "content": "actually quite rough when zoomed in. The curvature evaluated on such a rough surface can be too", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "score": 1.0, + "content": "noisy to be used for training. To alleviate this issue, we only compute the curvature regularization in", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 552, + 505, + 564 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 394, + 564 + ], + "score": 1.0, + "content": "areas where the curvature of the level set is less than a certain threshold", + "type": "text" + }, + { + "bbox": [ + 395, + 554, + 402, + 562 + ], + "score": 0.69, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 552, + 505, + 564 + ], + "score": 1.0, + "content": ". Formally, we define this", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 563, + 504, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 136, + 577 + ], + "score": 1.0, + "content": "area as", + "type": "text" + }, + { + "bbox": [ + 137, + 563, + 292, + 576 + ], + "score": 0.91, + "content": "V _ { \\tau } = \\{ \\mathbf { x } \\in U | \\operatorname* { m a x } ( | \\kappa _ { G _ { \\theta } } | , | \\kappa _ { F } | ) < \\tau \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 292, + 563, + 492, + 577 + ], + "score": 1.0, + "content": ". We use rejection sampling to sample points from", + "type": "text" + }, + { + "bbox": [ + 492, + 563, + 504, + 574 + ], + "score": 0.84, + "content": "V _ { \\tau }", + "type": "inline_equation" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 574, + 272, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 272, + 587 + ], + "score": 1.0, + "content": "when computing the loss during training.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 31, + "bbox_fs": [ + 105, + 508, + 506, + 587 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 601, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 601, + 506, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 601, + 506, + 614 + ], + "score": 1.0, + "content": "Results. We follow prior works [20, 76] to use Armadillo [40] and a sphere with one half of it", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 613, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 505, + 624 + ], + "score": 1.0, + "content": "corrupted by Gaussian noise. We compare our algorithm to two baselines. The first baseline directly", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 623, + 506, + 636 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 506, + 636 + ], + "score": 1.0, + "content": "applies the smoothing algorithm developed by Taubin [76] to the mesh extracted from the neural field", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 634, + 506, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 506, + 647 + ], + "score": 1.0, + "content": "using Marching cube [44]. The second baseline applies the filtering algorithms on meshes simplified", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 644, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 658 + ], + "score": 1.0, + "content": "by quadratic decimation [27]. The input neural fields are created following the procedure of Park", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "score": 1.0, + "content": "et al. [56]. The results are shown in Figure 2. The first baseline fails to smooth or sharpen the surface", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 667, + 506, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 506, + 680 + ], + "score": 1.0, + "content": "appropriately. It only modifies the surface with high-frequency noise. While the second baseline can", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 678, + 504, + 690 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 504, + 690 + ], + "score": 1.0, + "content": "filter the surface correctly, it introduces discretization artifacts due to the decimation process. This", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "suggests it is challenging to filter the neural field surface with mesh processing algorithms since these", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 700, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 700, + 505, + 712 + ], + "score": 1.0, + "content": "algorithms are sensitive to the quality of surface discretization. On the other hand, our algorithm can", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 711, + 488, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 488, + 723 + ], + "score": 1.0, + "content": "produce good filtering results without the need to maintain a good discretization of the surface.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 601, + 506, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 106, + 71, + 191, + 84 + ], + "lines": [ + { + "bbox": [ + 104, + 69, + 192, + 87 + ], + "spans": [ + { + "bbox": [ + 104, + 69, + 192, + 87 + ], + "score": 1.0, + "content": "5 Deformation", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 95, + 506, + 173 + ], + "lines": [ + { + "bbox": [ + 104, + 94, + 508, + 111 + ], + "spans": [ + { + "bbox": [ + 104, + 94, + 383, + 111 + ], + "score": 1.0, + "content": "To deform a shape, the user will choose a set of deformation handles", + "type": "text" + }, + { + "bbox": [ + 383, + 96, + 417, + 108 + ], + "score": 0.92, + "content": "\\{ { \\bf h } _ { i } \\} _ { i = 1 } ^ { n }", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 94, + 491, + 111 + ], + "score": 1.0, + "content": ". For each handles", + "type": "text" + }, + { + "bbox": [ + 491, + 96, + 502, + 107 + ], + "score": 0.86, + "content": "\\mathbf { h } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 94, + 508, + 111 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 106, + 506, + 119 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 252, + 119 + ], + "score": 1.0, + "content": "the user will specify a target location", + "type": "text" + }, + { + "bbox": [ + 252, + 108, + 262, + 118 + ], + "score": 0.87, + "content": "\\mathbf { t } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 106, + 506, + 119 + ], + "score": 1.0, + "content": "describing where the handle will be dragged to. Users can set", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 118, + 505, + 130 + ], + "spans": [ + { + "bbox": [ + 106, + 118, + 138, + 129 + ], + "score": 0.91, + "content": "\\mathbf { t } _ { i } = \\mathbf { h } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 138, + 118, + 505, + 130 + ], + "score": 1.0, + "content": "to enforce a part of the surface to be unchanged. Given this input, there are two goals for the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 129, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 106, + 129, + 506, + 141 + ], + "score": 1.0, + "content": "shape deformation algorithm: 1) satisfying user inputs and 2) ensuring that the deformation resembles", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 138, + 505, + 152 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 505, + 152 + ], + "score": 1.0, + "content": "the natural behavior of real objects. The input shape will be represented by the zero-isosurface", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 151, + 506, + 163 + ], + "spans": [ + { + "bbox": [ + 106, + 151, + 176, + 163 + ], + "score": 1.0, + "content": "of a neural field", + "type": "text" + }, + { + "bbox": [ + 176, + 151, + 185, + 160 + ], + "score": 0.83, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 185, + 151, + 461, + 163 + ], + "score": 1.0, + "content": "in our setting. The algorithm must therefore output a neural field", + "type": "text" + }, + { + "bbox": [ + 461, + 151, + 474, + 162 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 151, + 506, + 163 + ], + "score": 1.0, + "content": "whose", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 161, + 468, + 174 + ], + "spans": [ + { + "bbox": [ + 106, + 161, + 468, + 174 + ], + "score": 1.0, + "content": "zero-isosurface represents the deformed shape that satisfies the aforementioned two goals.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 105, + 177, + 480, + 189 + ], + "lines": [ + { + "bbox": [ + 105, + 176, + 480, + 191 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 480, + 191 + ], + "score": 1.0, + "content": "In this setting, deformation can be formulated as solving a constrained optimization problem:", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "interline_equation", + "bbox": [ + 183, + 194, + 425, + 212 + ], + "lines": [ + { + "bbox": [ + 183, + 194, + 425, + 212 + ], + "spans": [ + { + "bbox": [ + 183, + 194, + 425, + 212 + ], + "score": 0.9, + "content": "\\operatorname* { m i n } _ { \\theta } \\ \\mathcal { L } _ { d f m } ( G _ { \\theta } , F ) \\quad \\mathrm { s . t . } \\ \\mathcal { L } _ { c o n s t } ( G _ { \\theta } , \\mathbf { t } _ { i } , \\mathbf { h } _ { i } ) = 0 , 1 \\leq i \\leq n ,", + "type": "interline_equation", + "image_path": "d2141fab6172c932163522b1a6abc7db12b2a399d6dea33ec0fdf70bc739ed9e.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 183, + 194, + 425, + 212 + ], + "spans": [], + "index": 9 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 218, + 506, + 241 + ], + "lines": [ + { + "bbox": [ + 105, + 217, + 505, + 231 + ], + "spans": [ + { + "bbox": [ + 105, + 217, + 193, + 231 + ], + "score": 1.0, + "content": "where the objective", + "type": "text" + }, + { + "bbox": [ + 194, + 218, + 249, + 231 + ], + "score": 0.92, + "content": "\\mathcal { L } _ { d f m } ( G _ { \\theta } , F )", + "type": "inline_equation" + }, + { + "bbox": [ + 249, + 217, + 505, + 231 + ], + "score": 1.0, + "content": "measures how natural the deformation is. The constraints", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 107, + 229, + 416, + 243 + ], + "spans": [ + { + "bbox": [ + 107, + 230, + 199, + 242 + ], + "score": 0.91, + "content": "\\mathcal { L } _ { c o n s t } ( G _ { \\theta } , \\mathbf { t } _ { i } , \\mathbf { h } _ { i } ) = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 229, + 416, + 243 + ], + "score": 1.0, + "content": "ensure that the result deformation matches user input.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 107, + 245, + 505, + 312 + ], + "lines": [ + { + "bbox": [ + 106, + 246, + 505, + 258 + ], + "spans": [ + { + "bbox": [ + 106, + 246, + 505, + 258 + ], + "score": 1.0, + "content": "One way to ensure a natural-looking deformation is to assume that the surface behaves like a thin", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 256, + 505, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 256, + 505, + 270 + ], + "score": 1.0, + "content": "elastic shell, which is resistant to stretching and bending [1, 70]. Traditional mesh-based algorithms", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 268, + 505, + 281 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 505, + 281 + ], + "score": 1.0, + "content": "model elasticity by minimizing the thin shell energy that penalizes stretching or bending happened", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 279, + 505, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 279, + 505, + 291 + ], + "score": 1.0, + "content": "to any local patch. Naively adapting such training objectives from mesh-based algorithms to neural", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 289, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 505, + 302 + ], + "score": 1.0, + "content": "fields is challenging because these algorithms assume dense correspondences between two surfaces", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 301, + 278, + 313 + ], + "spans": [ + { + "bbox": [ + 105, + 301, + 278, + 313 + ], + "score": 1.0, + "content": "and efficient access to geodesic neighbors.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14.5 + }, + { + "type": "text", + "bbox": [ + 106, + 316, + 505, + 394 + ], + "lines": [ + { + "bbox": [ + 105, + 316, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 316, + 505, + 330 + ], + "score": 1.0, + "content": "In this section, we will address these challenges by following strategy. To measure how much bending", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 327, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 505, + 340 + ], + "score": 1.0, + "content": "or stretching happened to the whole surface, we will first divide the surface into infinitesimal patches", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 338, + 505, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 505, + 352 + ], + "score": 1.0, + "content": "and then sum the amount of bending or stretching that happened to each patch. To achieve that, we", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 348, + 506, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 506, + 363 + ], + "score": 1.0, + "content": "first develop a sampling schema to sample these infinitesimal patches uniformly from the input shapes", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 361, + 505, + 373 + ], + "spans": [ + { + "bbox": [ + 106, + 361, + 505, + 373 + ], + "score": 1.0, + "content": "(Sec 5.1). Then we warp the input shape with an invertible neural network to achieve correspondences", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 372, + 506, + 384 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 506, + 384 + ], + "score": 1.0, + "content": "between the input and output surfaces (Sec 5.2). Finally, we derive ways that measure the amount of", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 382, + 409, + 395 + ], + "spans": [ + { + "bbox": [ + 106, + 382, + 409, + 395 + ], + "score": 1.0, + "content": "bending and stretching between two infinitesimal surface patches (Sec 5.3).", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21 + }, + { + "type": "title", + "bbox": [ + 107, + 406, + 171, + 419 + ], + "lines": [ + { + "bbox": [ + 104, + 404, + 173, + 422 + ], + "spans": [ + { + "bbox": [ + 104, + 404, + 173, + 422 + ], + "score": 1.0, + "content": "5.1 Sampling", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 107, + 426, + 337, + 536 + ], + "lines": [ + { + "bbox": [ + 106, + 426, + 338, + 439 + ], + "spans": [ + { + "bbox": [ + 106, + 426, + 338, + 439 + ], + "score": 1.0, + "content": "Our first step is to sample infinitesimal surface patches uni-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 438, + 337, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 337, + 450 + ], + "score": 1.0, + "content": "formly to the surface area from the zero-isosurface of the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 448, + 338, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 338, + 461 + ], + "score": 1.0, + "content": "neural field. Each infinitesimal surface patch can be rep-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 460, + 336, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 336, + 471 + ], + "score": 1.0, + "content": "resented by a surface point and its local derivatives. With", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 470, + 337, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 337, + 483 + ], + "score": 1.0, + "content": "this said, the problem amounts to sampling points from", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 481, + 337, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 481, + 337, + 493 + ], + "score": 1.0, + "content": "the zero-isosurface. Formally, we are given a neural field", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 107, + 492, + 337, + 505 + ], + "spans": [ + { + "bbox": [ + 107, + 493, + 115, + 502 + ], + "score": 0.78, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 116, + 492, + 337, + 505 + ], + "score": 1.0, + "content": "that approximates the signed distance field of the input", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 503, + 337, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 503, + 337, + 516 + ], + "score": 1.0, + "content": "shape. The goal is to find a way to sample an arbitrary", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 513, + 337, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 271, + 527 + ], + "score": 1.0, + "content": "number of points on its zero-isosurface", + "type": "text" + }, + { + "bbox": [ + 272, + 515, + 291, + 525 + ], + "score": 0.91, + "content": "\\mathcal { M } _ { F }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 513, + 337, + 527 + ], + "score": 1.0, + "content": ". One way", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 525, + 337, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 198, + 537 + ], + "score": 1.0, + "content": "to sample points from", + "type": "text" + }, + { + "bbox": [ + 198, + 525, + 218, + 536 + ], + "score": 0.9, + "content": "\\mathcal { M } _ { F }", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 525, + 337, + 537 + ], + "score": 1.0, + "content": "is to run Langevin dynamics", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 30.5 + }, + { + "type": "image", + "bbox": [ + 344, + 429, + 504, + 502 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 344, + 429, + 504, + 502 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 344, + 429, + 504, + 502 + ], + "spans": [ + { + "bbox": [ + 344, + 429, + 504, + 502 + ], + "score": 0.963, + "type": "image", + "image_path": "1bb5cd9809445b92975f25d3de02307121f0571a65d61bf8b055406cdc447ce9.jpg" + } + ] + } + ], + "index": 38, + "virtual_lines": [ + { + "bbox": [ + 344, + 429, + 504, + 443.6 + ], + "spans": [], + "index": 36 + }, + { + "bbox": [ + 344, + 443.6, + 504, + 458.20000000000005 + ], + "spans": [], + "index": 37 + }, + { + "bbox": [ + 344, + 458.20000000000005, + 504, + 472.80000000000007 + ], + "spans": [], + "index": 38 + }, + { + "bbox": [ + 344, + 472.80000000000007, + 504, + 487.4000000000001 + ], + "spans": [], + "index": 39 + }, + { + "bbox": [ + 344, + 487.4000000000001, + 504, + 502.0000000000001 + ], + "spans": [], + "index": 40 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 343, + 507, + 505, + 529 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 343, + 505, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 343, + 505, + 505, + 520 + ], + "score": 1.0, + "content": "Figure 3: Sampling from dino. L: no", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 343, + 516, + 482, + 531 + ], + "spans": [ + { + "bbox": [ + 343, + 516, + 482, + 531 + ], + "score": 1.0, + "content": "rejection; R: ours (with rejection).", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41.5 + } + ], + "index": 39.75 + }, + { + "type": "text", + "bbox": [ + 106, + 536, + 505, + 603 + ], + "lines": [ + { + "bbox": [ + 105, + 535, + 505, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 231, + 549 + ], + "score": 1.0, + "content": "using the gradient of the field", + "type": "text" + }, + { + "bbox": [ + 232, + 537, + 241, + 546 + ], + "score": 0.8, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 535, + 276, + 549 + ], + "score": 1.0, + "content": "[5, 13]:", + "type": "text" + }, + { + "bbox": [ + 276, + 536, + 391, + 548 + ], + "score": 0.69, + "content": "\\mathbf { x } _ { t + 1 } \\overset { \\cdot } { = } \\tilde { \\mathbf { x } } _ { t } - F ( \\tilde { \\mathbf { x } } _ { t } ) n _ { F } ( \\tilde { \\mathbf { x } } _ { t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 391, + 535, + 403, + 549 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 403, + 536, + 471, + 548 + ], + "score": 0.85, + "content": "\\tilde { \\mathbf { x } } _ { t } \\sim \\mathcal { N } ( \\mathbf { x } _ { t } , \\sigma \\mathbf { I } )", + "type": "inline_equation" + }, + { + "bbox": [ + 472, + 535, + 476, + 549 + ], + "score": 1.0, + "content": ".", + "type": "text" + }, + { + "bbox": [ + 476, + 537, + 488, + 547 + ], + "score": 0.74, + "content": "\\mathbf { x } _ { \\mathrm { 0 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 489, + 535, + 505, + 549 + ], + "score": 1.0, + "content": "are", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 104, + 545, + 506, + 560 + ], + "spans": [ + { + "bbox": [ + 104, + 545, + 278, + 560 + ], + "score": 1.0, + "content": "initialized by sampling uniformly within", + "type": "text" + }, + { + "bbox": [ + 278, + 547, + 311, + 559 + ], + "score": 0.9, + "content": "[ - 1 , 1 ] ^ { 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 545, + 506, + 560 + ], + "score": 1.0, + "content": ". Here we also leverage an SDF property: the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 557, + 505, + 571 + ], + "spans": [ + { + "bbox": [ + 105, + 557, + 201, + 571 + ], + "score": 1.0, + "content": "closest surface point to", + "type": "text" + }, + { + "bbox": [ + 201, + 560, + 209, + 568 + ], + "score": 0.47, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 209, + 557, + 293, + 571 + ], + "score": 1.0, + "content": "can be computed by", + "type": "text" + }, + { + "bbox": [ + 293, + 558, + 354, + 570 + ], + "score": 0.9, + "content": "{ \\bf x } - { \\bf n } ( { \\bf x } ) F ( { \\bf x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 557, + 505, + 571 + ], + "score": 1.0, + "content": "(Sec 3). While this process produces", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 569, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 506, + 581 + ], + "score": 1.0, + "content": "points guaranteed to be on the zero-isosurface, the mixing time of the procedure is very long without", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 580, + 506, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 580, + 506, + 592 + ], + "score": 1.0, + "content": "appropriate coarse-to-fine annealing [68]. Running this process for limited iterations results in point", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 591, + 504, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 504, + 603 + ], + "score": 1.0, + "content": "samples that are concentrating near the high curvature area, as shown on the left side of Figure 5.1.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 45.5 + }, + { + "type": "text", + "bbox": [ + 106, + 607, + 505, + 662 + ], + "lines": [ + { + "bbox": [ + 105, + 605, + 506, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 374, + 620 + ], + "score": 1.0, + "content": "To alleviate this issue, we instantiate the sampling procedure with", + "type": "text" + }, + { + "bbox": [ + 374, + 609, + 386, + 618 + ], + "score": 0.85, + "content": "\\mathbf { x } _ { \\mathrm { 0 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 605, + 506, + 620 + ], + "score": 1.0, + "content": "sampled from a rough shape.", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 617, + 505, + 630 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 505, + 630 + ], + "score": 1.0, + "content": "This can be done by first sampling uniformly from the bounded space and rejecting points that are", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 629, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 106, + 629, + 245, + 641 + ], + "score": 1.0, + "content": "too far away from the isosurface:", + "type": "text" + }, + { + "bbox": [ + 245, + 629, + 385, + 641 + ], + "score": 0.93, + "content": "\\mathbf { x } _ { 0 } \\sim \\{ \\mathbf { x } \\in U ( - 1 , 1 ) | F ( \\mathbf { x } ) < \\tau _ { s } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 629, + 450, + 641 + ], + "score": 1.0, + "content": ". We found that", + "type": "text" + }, + { + "bbox": [ + 451, + 631, + 461, + 640 + ], + "score": 0.84, + "content": "\\tau _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 461, + 629, + 505, + 641 + ], + "score": 1.0, + "content": "can be set", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 639, + 505, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 505, + 653 + ], + "score": 1.0, + "content": "to a relatively large number (e.g., about 0.1). This prevents high rejection rates without sacrificing", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 650, + 415, + 664 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 415, + 664 + ], + "score": 1.0, + "content": "sampling quality. Figure 5.1 shows that our method creates uniform samples.", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 51 + }, + { + "type": "text", + "bbox": [ + 107, + 667, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 667, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 679 + ], + "score": 1.0, + "content": "We quantitatively evaluate the effectiveness of the sampling scheme. Specifically, we compare our", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 105, + 678, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 378, + 691 + ], + "score": 1.0, + "content": "sampling scheme with directly applying Langevin dynamics [13] (", + "type": "text" + }, + { + "bbox": [ + 378, + 679, + 392, + 688 + ], + "score": 0.68, + "content": "L D", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 678, + 505, + 691 + ], + "score": 1.0, + "content": "in Table 1). To do that, we", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 105, + 687, + 505, + 703 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 703 + ], + "score": 1.0, + "content": "compute the Chamfer Distance (CD) and Earth Mover Distance (EMD) between points sampled by", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 105, + 698, + 507, + 714 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 507, + 714 + ], + "score": 1.0, + "content": "the valuated algorithms and points sampled uniformly from the extracted mesh. For both metrics,", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 105, + 710, + 507, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 507, + 724 + ], + "score": 1.0, + "content": "lower values indicate better performance Since larger surfaces can lead to larger CD and EMD values,", + "type": "text" + } + ], + "index": 58 + } + ], + "index": 56 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 741, + 308, + 750 + ], + "lines": [ + { + "bbox": [ + 302, + 740, + 309, + 753 + ], + "spans": [ + { + "bbox": [ + 302, + 740, + 309, + 753 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 106, + 71, + 191, + 84 + ], + "lines": [ + { + "bbox": [ + 104, + 69, + 192, + 87 + ], + "spans": [ + { + "bbox": [ + 104, + 69, + 192, + 87 + ], + "score": 1.0, + "content": "5 Deformation", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 95, + 506, + 173 + ], + "lines": [ + { + "bbox": [ + 104, + 94, + 508, + 111 + ], + "spans": [ + { + "bbox": [ + 104, + 94, + 383, + 111 + ], + "score": 1.0, + "content": "To deform a shape, the user will choose a set of deformation handles", + "type": "text" + }, + { + "bbox": [ + 383, + 96, + 417, + 108 + ], + "score": 0.92, + "content": "\\{ { \\bf h } _ { i } \\} _ { i = 1 } ^ { n }", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 94, + 491, + 111 + ], + "score": 1.0, + "content": ". For each handles", + "type": "text" + }, + { + "bbox": [ + 491, + 96, + 502, + 107 + ], + "score": 0.86, + "content": "\\mathbf { h } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 94, + 508, + 111 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 106, + 506, + 119 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 252, + 119 + ], + "score": 1.0, + "content": "the user will specify a target location", + "type": "text" + }, + { + "bbox": [ + 252, + 108, + 262, + 118 + ], + "score": 0.87, + "content": "\\mathbf { t } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 106, + 506, + 119 + ], + "score": 1.0, + "content": "describing where the handle will be dragged to. Users can set", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 118, + 505, + 130 + ], + "spans": [ + { + "bbox": [ + 106, + 118, + 138, + 129 + ], + "score": 0.91, + "content": "\\mathbf { t } _ { i } = \\mathbf { h } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 138, + 118, + 505, + 130 + ], + "score": 1.0, + "content": "to enforce a part of the surface to be unchanged. Given this input, there are two goals for the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 129, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 106, + 129, + 506, + 141 + ], + "score": 1.0, + "content": "shape deformation algorithm: 1) satisfying user inputs and 2) ensuring that the deformation resembles", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 138, + 505, + 152 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 505, + 152 + ], + "score": 1.0, + "content": "the natural behavior of real objects. The input shape will be represented by the zero-isosurface", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 151, + 506, + 163 + ], + "spans": [ + { + "bbox": [ + 106, + 151, + 176, + 163 + ], + "score": 1.0, + "content": "of a neural field", + "type": "text" + }, + { + "bbox": [ + 176, + 151, + 185, + 160 + ], + "score": 0.83, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 185, + 151, + 461, + 163 + ], + "score": 1.0, + "content": "in our setting. The algorithm must therefore output a neural field", + "type": "text" + }, + { + "bbox": [ + 461, + 151, + 474, + 162 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 151, + 506, + 163 + ], + "score": 1.0, + "content": "whose", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 161, + 468, + 174 + ], + "spans": [ + { + "bbox": [ + 106, + 161, + 468, + 174 + ], + "score": 1.0, + "content": "zero-isosurface represents the deformed shape that satisfies the aforementioned two goals.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4, + "bbox_fs": [ + 104, + 94, + 508, + 174 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 177, + 480, + 189 + ], + "lines": [ + { + "bbox": [ + 105, + 176, + 480, + 191 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 480, + 191 + ], + "score": 1.0, + "content": "In this setting, deformation can be formulated as solving a constrained optimization problem:", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 176, + 480, + 191 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 183, + 194, + 425, + 212 + ], + "lines": [ + { + "bbox": [ + 183, + 194, + 425, + 212 + ], + "spans": [ + { + "bbox": [ + 183, + 194, + 425, + 212 + ], + "score": 0.9, + "content": "\\operatorname* { m i n } _ { \\theta } \\ \\mathcal { L } _ { d f m } ( G _ { \\theta } , F ) \\quad \\mathrm { s . t . } \\ \\mathcal { L } _ { c o n s t } ( G _ { \\theta } , \\mathbf { t } _ { i } , \\mathbf { h } _ { i } ) = 0 , 1 \\leq i \\leq n ,", + "type": "interline_equation", + "image_path": "d2141fab6172c932163522b1a6abc7db12b2a399d6dea33ec0fdf70bc739ed9e.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 183, + 194, + 425, + 212 + ], + "spans": [], + "index": 9 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 218, + 506, + 241 + ], + "lines": [ + { + "bbox": [ + 105, + 217, + 505, + 231 + ], + "spans": [ + { + "bbox": [ + 105, + 217, + 193, + 231 + ], + "score": 1.0, + "content": "where the objective", + "type": "text" + }, + { + "bbox": [ + 194, + 218, + 249, + 231 + ], + "score": 0.92, + "content": "\\mathcal { L } _ { d f m } ( G _ { \\theta } , F )", + "type": "inline_equation" + }, + { + "bbox": [ + 249, + 217, + 505, + 231 + ], + "score": 1.0, + "content": "measures how natural the deformation is. The constraints", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 107, + 229, + 416, + 243 + ], + "spans": [ + { + "bbox": [ + 107, + 230, + 199, + 242 + ], + "score": 0.91, + "content": "\\mathcal { L } _ { c o n s t } ( G _ { \\theta } , \\mathbf { t } _ { i } , \\mathbf { h } _ { i } ) = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 229, + 416, + 243 + ], + "score": 1.0, + "content": "ensure that the result deformation matches user input.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5, + "bbox_fs": [ + 105, + 217, + 505, + 243 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 245, + 505, + 312 + ], + "lines": [ + { + "bbox": [ + 106, + 246, + 505, + 258 + ], + "spans": [ + { + "bbox": [ + 106, + 246, + 505, + 258 + ], + "score": 1.0, + "content": "One way to ensure a natural-looking deformation is to assume that the surface behaves like a thin", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 256, + 505, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 256, + 505, + 270 + ], + "score": 1.0, + "content": "elastic shell, which is resistant to stretching and bending [1, 70]. Traditional mesh-based algorithms", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 268, + 505, + 281 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 505, + 281 + ], + "score": 1.0, + "content": "model elasticity by minimizing the thin shell energy that penalizes stretching or bending happened", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 279, + 505, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 279, + 505, + 291 + ], + "score": 1.0, + "content": "to any local patch. Naively adapting such training objectives from mesh-based algorithms to neural", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 289, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 505, + 302 + ], + "score": 1.0, + "content": "fields is challenging because these algorithms assume dense correspondences between two surfaces", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 301, + 278, + 313 + ], + "spans": [ + { + "bbox": [ + 105, + 301, + 278, + 313 + ], + "score": 1.0, + "content": "and efficient access to geodesic neighbors.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14.5, + "bbox_fs": [ + 105, + 246, + 505, + 313 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 316, + 505, + 394 + ], + "lines": [ + { + "bbox": [ + 105, + 316, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 316, + 505, + 330 + ], + "score": 1.0, + "content": "In this section, we will address these challenges by following strategy. To measure how much bending", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 327, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 505, + 340 + ], + "score": 1.0, + "content": "or stretching happened to the whole surface, we will first divide the surface into infinitesimal patches", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 338, + 505, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 505, + 352 + ], + "score": 1.0, + "content": "and then sum the amount of bending or stretching that happened to each patch. To achieve that, we", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 348, + 506, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 506, + 363 + ], + "score": 1.0, + "content": "first develop a sampling schema to sample these infinitesimal patches uniformly from the input shapes", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 361, + 505, + 373 + ], + "spans": [ + { + "bbox": [ + 106, + 361, + 505, + 373 + ], + "score": 1.0, + "content": "(Sec 5.1). Then we warp the input shape with an invertible neural network to achieve correspondences", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 372, + 506, + 384 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 506, + 384 + ], + "score": 1.0, + "content": "between the input and output surfaces (Sec 5.2). Finally, we derive ways that measure the amount of", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 382, + 409, + 395 + ], + "spans": [ + { + "bbox": [ + 106, + 382, + 409, + 395 + ], + "score": 1.0, + "content": "bending and stretching between two infinitesimal surface patches (Sec 5.3).", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 316, + 506, + 395 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 406, + 171, + 419 + ], + "lines": [ + { + "bbox": [ + 104, + 404, + 173, + 422 + ], + "spans": [ + { + "bbox": [ + 104, + 404, + 173, + 422 + ], + "score": 1.0, + "content": "5.1 Sampling", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 107, + 426, + 337, + 536 + ], + "lines": [ + { + "bbox": [ + 106, + 426, + 338, + 439 + ], + "spans": [ + { + "bbox": [ + 106, + 426, + 338, + 439 + ], + "score": 1.0, + "content": "Our first step is to sample infinitesimal surface patches uni-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 438, + 337, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 337, + 450 + ], + "score": 1.0, + "content": "formly to the surface area from the zero-isosurface of the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 448, + 338, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 338, + 461 + ], + "score": 1.0, + "content": "neural field. Each infinitesimal surface patch can be rep-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 460, + 336, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 336, + 471 + ], + "score": 1.0, + "content": "resented by a surface point and its local derivatives. With", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 470, + 337, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 337, + 483 + ], + "score": 1.0, + "content": "this said, the problem amounts to sampling points from", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 481, + 337, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 481, + 337, + 493 + ], + "score": 1.0, + "content": "the zero-isosurface. Formally, we are given a neural field", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 107, + 492, + 337, + 505 + ], + "spans": [ + { + "bbox": [ + 107, + 493, + 115, + 502 + ], + "score": 0.78, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 116, + 492, + 337, + 505 + ], + "score": 1.0, + "content": "that approximates the signed distance field of the input", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 503, + 337, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 503, + 337, + 516 + ], + "score": 1.0, + "content": "shape. The goal is to find a way to sample an arbitrary", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 513, + 337, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 271, + 527 + ], + "score": 1.0, + "content": "number of points on its zero-isosurface", + "type": "text" + }, + { + "bbox": [ + 272, + 515, + 291, + 525 + ], + "score": 0.91, + "content": "\\mathcal { M } _ { F }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 513, + 337, + 527 + ], + "score": 1.0, + "content": ". One way", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 525, + 337, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 198, + 537 + ], + "score": 1.0, + "content": "to sample points from", + "type": "text" + }, + { + "bbox": [ + 198, + 525, + 218, + 536 + ], + "score": 0.9, + "content": "\\mathcal { M } _ { F }", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 525, + 337, + 537 + ], + "score": 1.0, + "content": "is to run Langevin dynamics", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 535, + 505, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 231, + 549 + ], + "score": 1.0, + "content": "using the gradient of the field", + "type": "text" + }, + { + "bbox": [ + 232, + 537, + 241, + 546 + ], + "score": 0.8, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 535, + 276, + 549 + ], + "score": 1.0, + "content": "[5, 13]:", + "type": "text" + }, + { + "bbox": [ + 276, + 536, + 391, + 548 + ], + "score": 0.69, + "content": "\\mathbf { x } _ { t + 1 } \\overset { \\cdot } { = } \\tilde { \\mathbf { x } } _ { t } - F ( \\tilde { \\mathbf { x } } _ { t } ) n _ { F } ( \\tilde { \\mathbf { x } } _ { t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 391, + 535, + 403, + 549 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 403, + 536, + 471, + 548 + ], + "score": 0.85, + "content": "\\tilde { \\mathbf { x } } _ { t } \\sim \\mathcal { N } ( \\mathbf { x } _ { t } , \\sigma \\mathbf { I } )", + "type": "inline_equation" + }, + { + "bbox": [ + 472, + 535, + 476, + 549 + ], + "score": 1.0, + "content": ".", + "type": "text" + }, + { + "bbox": [ + 476, + 537, + 488, + 547 + ], + "score": 0.74, + "content": "\\mathbf { x } _ { \\mathrm { 0 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 489, + 535, + 505, + 549 + ], + "score": 1.0, + "content": "are", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 104, + 545, + 506, + 560 + ], + "spans": [ + { + "bbox": [ + 104, + 545, + 278, + 560 + ], + "score": 1.0, + "content": "initialized by sampling uniformly within", + "type": "text" + }, + { + "bbox": [ + 278, + 547, + 311, + 559 + ], + "score": 0.9, + "content": "[ - 1 , 1 ] ^ { 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 545, + 506, + 560 + ], + "score": 1.0, + "content": ". Here we also leverage an SDF property: the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 557, + 505, + 571 + ], + "spans": [ + { + "bbox": [ + 105, + 557, + 201, + 571 + ], + "score": 1.0, + "content": "closest surface point to", + "type": "text" + }, + { + "bbox": [ + 201, + 560, + 209, + 568 + ], + "score": 0.47, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 209, + 557, + 293, + 571 + ], + "score": 1.0, + "content": "can be computed by", + "type": "text" + }, + { + "bbox": [ + 293, + 558, + 354, + 570 + ], + "score": 0.9, + "content": "{ \\bf x } - { \\bf n } ( { \\bf x } ) F ( { \\bf x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 557, + 505, + 571 + ], + "score": 1.0, + "content": "(Sec 3). While this process produces", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 569, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 506, + 581 + ], + "score": 1.0, + "content": "points guaranteed to be on the zero-isosurface, the mixing time of the procedure is very long without", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 580, + 506, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 580, + 506, + 592 + ], + "score": 1.0, + "content": "appropriate coarse-to-fine annealing [68]. Running this process for limited iterations results in point", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 591, + 504, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 504, + 603 + ], + "score": 1.0, + "content": "samples that are concentrating near the high curvature area, as shown on the left side of Figure 5.1.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 426, + 338, + 537 + ] + }, + { + "type": "image", + "bbox": [ + 344, + 429, + 504, + 502 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 344, + 429, + 504, + 502 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 344, + 429, + 504, + 502 + ], + "spans": [ + { + "bbox": [ + 344, + 429, + 504, + 502 + ], + "score": 0.963, + "type": "image", + "image_path": "1bb5cd9809445b92975f25d3de02307121f0571a65d61bf8b055406cdc447ce9.jpg" + } + ] + } + ], + "index": 38, + "virtual_lines": [ + { + "bbox": [ + 344, + 429, + 504, + 443.6 + ], + "spans": [], + "index": 36 + }, + { + "bbox": [ + 344, + 443.6, + 504, + 458.20000000000005 + ], + "spans": [], + "index": 37 + }, + { + "bbox": [ + 344, + 458.20000000000005, + 504, + 472.80000000000007 + ], + "spans": [], + "index": 38 + }, + { + "bbox": [ + 344, + 472.80000000000007, + 504, + 487.4000000000001 + ], + "spans": [], + "index": 39 + }, + { + "bbox": [ + 344, + 487.4000000000001, + 504, + 502.0000000000001 + ], + "spans": [], + "index": 40 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 343, + 507, + 505, + 529 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 343, + 505, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 343, + 505, + 505, + 520 + ], + "score": 1.0, + "content": "Figure 3: Sampling from dino. L: no", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 343, + 516, + 482, + 531 + ], + "spans": [ + { + "bbox": [ + 343, + 516, + 482, + 531 + ], + "score": 1.0, + "content": "rejection; R: ours (with rejection).", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41.5 + } + ], + "index": 39.75 + }, + { + "type": "text", + "bbox": [ + 106, + 536, + 505, + 603 + ], + "lines": [], + "index": 45.5, + "bbox_fs": [ + 104, + 535, + 506, + 603 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 607, + 505, + 662 + ], + "lines": [ + { + "bbox": [ + 105, + 605, + 506, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 374, + 620 + ], + "score": 1.0, + "content": "To alleviate this issue, we instantiate the sampling procedure with", + "type": "text" + }, + { + "bbox": [ + 374, + 609, + 386, + 618 + ], + "score": 0.85, + "content": "\\mathbf { x } _ { \\mathrm { 0 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 605, + 506, + 620 + ], + "score": 1.0, + "content": "sampled from a rough shape.", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 617, + 505, + 630 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 505, + 630 + ], + "score": 1.0, + "content": "This can be done by first sampling uniformly from the bounded space and rejecting points that are", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 629, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 106, + 629, + 245, + 641 + ], + "score": 1.0, + "content": "too far away from the isosurface:", + "type": "text" + }, + { + "bbox": [ + 245, + 629, + 385, + 641 + ], + "score": 0.93, + "content": "\\mathbf { x } _ { 0 } \\sim \\{ \\mathbf { x } \\in U ( - 1 , 1 ) | F ( \\mathbf { x } ) < \\tau _ { s } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 629, + 450, + 641 + ], + "score": 1.0, + "content": ". We found that", + "type": "text" + }, + { + "bbox": [ + 451, + 631, + 461, + 640 + ], + "score": 0.84, + "content": "\\tau _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 461, + 629, + 505, + 641 + ], + "score": 1.0, + "content": "can be set", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 639, + 505, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 505, + 653 + ], + "score": 1.0, + "content": "to a relatively large number (e.g., about 0.1). This prevents high rejection rates without sacrificing", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 650, + 415, + 664 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 415, + 664 + ], + "score": 1.0, + "content": "sampling quality. Figure 5.1 shows that our method creates uniform samples.", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 51, + "bbox_fs": [ + 105, + 605, + 506, + 664 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 667, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 667, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 679 + ], + "score": 1.0, + "content": "We quantitatively evaluate the effectiveness of the sampling scheme. Specifically, we compare our", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 105, + 678, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 378, + 691 + ], + "score": 1.0, + "content": "sampling scheme with directly applying Langevin dynamics [13] (", + "type": "text" + }, + { + "bbox": [ + 378, + 679, + 392, + 688 + ], + "score": 0.68, + "content": "L D", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 678, + 505, + 691 + ], + "score": 1.0, + "content": "in Table 1). To do that, we", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 105, + 687, + 505, + 703 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 703 + ], + "score": 1.0, + "content": "compute the Chamfer Distance (CD) and Earth Mover Distance (EMD) between points sampled by", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 105, + 698, + 507, + 714 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 507, + 714 + ], + "score": 1.0, + "content": "the valuated algorithms and points sampled uniformly from the extracted mesh. For both metrics,", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 105, + 710, + 507, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 507, + 724 + ], + "score": 1.0, + "content": "lower values indicate better performance Since larger surfaces can lead to larger CD and EMD values,", + "type": "text" + } + ], + "index": 58 + }, + { + "bbox": [ + 105, + 72, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 505, + 85 + ], + "score": 1.0, + "content": "we normalize the metrics by the values obtained by comparing two sets of uniform samples from the", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 351, + 96 + ], + "score": 1.0, + "content": "mesh (i.e., CDr and EMDr) The results show that initializing", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 351, + 85, + 363, + 95 + ], + "score": 0.84, + "content": "\\mathbf { x } _ { \\mathrm { 0 } }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 364, + 83, + 505, + 96 + ], + "score": 1.0, + "content": "by rejection sampling significantly", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 506, + 108 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 506, + 108 + ], + "score": 1.0, + "content": "improves both CD and EMD compared to naively applying Langevin dynamics, at a minor cost in", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 106, + 168, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 168, + 118 + ], + "score": 1.0, + "content": "sampling time.", + "type": "text", + "cross_page": true + } + ], + "index": 3 + } + ], + "index": 56, + "bbox_fs": [ + 105, + 667, + 507, + 724 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 117 + ], + "lines": [ + { + "bbox": [ + 105, + 72, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 505, + 85 + ], + "score": 1.0, + "content": "we normalize the metrics by the values obtained by comparing two sets of uniform samples from the", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 351, + 96 + ], + "score": 1.0, + "content": "mesh (i.e., CDr and EMDr) The results show that initializing", + "type": "text" + }, + { + "bbox": [ + 351, + 85, + 363, + 95 + ], + "score": 0.84, + "content": "\\mathbf { x } _ { \\mathrm { 0 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 364, + 83, + 505, + 96 + ], + "score": 1.0, + "content": "by rejection sampling significantly", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 506, + 108 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 506, + 108 + ], + "score": 1.0, + "content": "improves both CD and EMD compared to naively applying Langevin dynamics, at a minor cost in", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 106, + 168, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 168, + 118 + ], + "score": 1.0, + "content": "sampling time.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "title", + "bbox": [ + 107, + 133, + 253, + 145 + ], + "lines": [ + { + "bbox": [ + 106, + 133, + 253, + 146 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 253, + 146 + ], + "score": 1.0, + "content": "5.2 Invertible Deformation Field", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 107, + 155, + 337, + 255 + ], + "lines": [ + { + "bbox": [ + 106, + 154, + 338, + 167 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 338, + 167 + ], + "score": 1.0, + "content": "After we obtained surface points samples from zero isosur-", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 166, + 336, + 177 + ], + "spans": [ + { + "bbox": [ + 106, + 166, + 336, + 177 + ], + "score": 1.0, + "content": "faces of the input neural fields, the next step is to deform", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 177, + 337, + 189 + ], + "spans": [ + { + "bbox": [ + 106, + 177, + 337, + 189 + ], + "score": 1.0, + "content": "these surface points to the output shapes. One way to", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 188, + 337, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 188, + 337, + 199 + ], + "score": 1.0, + "content": "deform neural fields is to warp the coordinate space of", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 198, + 337, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 337, + 211 + ], + "score": 1.0, + "content": "the input network using a deformation field predicted by", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 210, + 338, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 210, + 176, + 222 + ], + "score": 1.0, + "content": "a neural network", + "type": "text" + }, + { + "bbox": [ + 177, + 210, + 190, + 221 + ], + "score": 0.86, + "content": "D _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 210, + 338, + 222 + ], + "score": 1.0, + "content": "[25, 43, 57]. 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Dino Armadillo
MetricsLDOursLDOurs
CDr (↓)1.541.041.361.02
EMDr (↓)3.381.153.301.08
Time0.150.210.120.18
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The inverse of such residual block can be", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 361, + 506, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 298, + 375 + ], + "score": 1.0, + "content": "computed by finding the fixed point of function", + "type": "text" + }, + { + "bbox": [ + 298, + 362, + 356, + 374 + ], + "score": 0.92, + "content": "y \\mapsto y - g ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 361, + 506, + 375 + ], + "score": 1.0, + "content": "[7]. 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Applying such architecture directly without modifi-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 411, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 106, + 411, + 506, + 423 + ], + "score": 1.0, + "content": "cation fails to produce deformations with many different local rotations. Recent research suggests", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 421, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 506, + 435 + ], + "score": 1.0, + "content": "that periodic functions are essential for coordinate MLPs to predict complex signals [47, 66, 74].", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 453, + 446 + ], + "score": 1.0, + "content": "Periodic functions are usually used as positional encoding or activations of the form", + "type": "text" + }, + { + "bbox": [ + 453, + 433, + 502, + 445 + ], + "score": 0.89, + "content": "\\sin ( a x + b )", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 433, + 506, + 446 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 444, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 132, + 456 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 132, + 446, + 139, + 454 + ], + "score": 0.72, + "content": "a", + "type": "inline_equation" + }, + { + "bbox": [ + 139, + 444, + 505, + 456 + ], + "score": 1.0, + "content": "controls the frequency of the activation. 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Dino Armadillo
MetricsLDOursLDOurs
CDr (↓)1.541.041.361.02
EMDr (↓)3.381.153.301.08
Time0.150.210.120.18
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This will allow us to", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 270, + 506, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 506, + 282 + ], + "score": 1.0, + "content": "create well-behaved one-to-one correspondences between points on the deform shape (i.e., x) and", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 281, + 506, + 293 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 233, + 293 + ], + "score": 1.0, + "content": "points on the input shape (i.e.,", + "type": "text" + }, + { + "bbox": [ + 234, + 281, + 263, + 293 + ], + "score": 0.91, + "content": "D _ { \\theta } ( \\mathbf { x } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 281, + 376, + 293 + ], + "score": 1.0, + "content": ". To achieve this, we make", + "type": "text" + }, + { + "bbox": [ + 377, + 281, + 391, + 292 + ], + "score": 0.89, + "content": "D _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 391, + 281, + 506, + 293 + ], + "score": 1.0, + "content": "to be an invertible network", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 292, + 336, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 336, + 304 + ], + "score": 1.0, + "content": "composed of a sequence of invertible residual blocks [7].", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 259, + 506, + 304 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 318, + 505, + 385 + ], + "lines": [ + { + "bbox": [ + 105, + 317, + 506, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 506, + 331 + ], + "score": 1.0, + "content": "Invertible residual block. Prior works [7, 17] have shown that a sufficient condition for the residual", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 328, + 507, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 328, + 132, + 343 + ], + "score": 1.0, + "content": "block", + "type": "text" + }, + { + "bbox": [ + 132, + 329, + 205, + 342 + ], + "score": 0.92, + "content": "f ( x ) = x + g ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 328, + 440, + 343 + ], + "score": 1.0, + "content": "to be invertible is that the Lipschitz constant of function", + "type": "text" + }, + { + "bbox": [ + 440, + 331, + 447, + 341 + ], + "score": 0.8, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 447, + 328, + 507, + 343 + ], + "score": 1.0, + "content": "is less than 1.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 236, + 353 + ], + "score": 1.0, + "content": "The architecture of the network", + "type": "text" + }, + { + "bbox": [ + 236, + 340, + 256, + 353 + ], + "score": 0.93, + "content": "g ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 340, + 506, + 353 + ], + "score": 1.0, + "content": "is usually composed of spectral normalized linear layers and", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 352, + 504, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 352, + 504, + 363 + ], + "score": 1.0, + "content": "Lipschitz continuous nonlinearities such as ELU [21]. The inverse of such residual block can be", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 361, + 506, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 298, + 375 + ], + "score": 1.0, + "content": "computed by finding the fixed point of function", + "type": "text" + }, + { + "bbox": [ + 298, + 362, + 356, + 374 + ], + "score": 0.92, + "content": "y \\mapsto y - g ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 361, + 506, + 375 + ], + "score": 1.0, + "content": "[7]. Intuitively, deforming using one", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 373, + 438, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 307, + 385 + ], + "score": 1.0, + "content": "invertible residual block amounts to moving point", + "type": "text" + }, + { + "bbox": [ + 308, + 376, + 315, + 383 + ], + "score": 0.76, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 315, + 374, + 414, + 385 + ], + "score": 1.0, + "content": "with deformation vector", + "type": "text" + }, + { + "bbox": [ + 415, + 373, + 434, + 385 + ], + "score": 0.93, + "content": "g ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 374, + 438, + 385 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 317, + 507, + 385 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 400, + 506, + 488 + ], + "lines": [ + { + "bbox": [ + 105, + 400, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 506, + 412 + ], + "score": 1.0, + "content": "Lipschitz continuous positional encoding. Applying such architecture directly without modifi-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 411, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 106, + 411, + 506, + 423 + ], + "score": 1.0, + "content": "cation fails to produce deformations with many different local rotations. Recent research suggests", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 421, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 506, + 435 + ], + "score": 1.0, + "content": "that periodic functions are essential for coordinate MLPs to predict complex signals [47, 66, 74].", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 453, + 446 + ], + "score": 1.0, + "content": "Periodic functions are usually used as positional encoding or activations of the form", + "type": "text" + }, + { + "bbox": [ + 453, + 433, + 502, + 445 + ], + "score": 0.89, + "content": "\\sin ( a x + b )", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 433, + 506, + 446 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 444, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 132, + 456 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 132, + 446, + 139, + 454 + ], + "score": 0.72, + "content": "a", + "type": "inline_equation" + }, + { + "bbox": [ + 139, + 444, + 505, + 456 + ], + "score": 1.0, + "content": "controls the frequency of the activation. To use such periodic function as part of the invertible", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 455, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 505, + 466 + ], + "score": 1.0, + "content": "residual block without restricting the frequency, we normalize the output of the periodic function", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 107, + 465, + 506, + 478 + ], + "spans": [ + { + "bbox": [ + 107, + 465, + 176, + 478 + ], + "score": 0.92, + "content": "\\sin ( a x + b ) | a | ^ { - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 176, + 465, + 506, + 478 + ], + "score": 1.0, + "content": ", bringing it is Lipschitz constant below 1. Formally, the positional encoding with", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 477, + 342, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 342, + 489 + ], + "score": 1.0, + "content": "normalized Lipschitz constant applied to one dimension is", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 34.5, + "bbox_fs": [ + 105, + 400, + 506, + 489 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 131, + 496, + 480, + 525 + ], + "lines": [ + { + "bbox": [ + 131, + 496, + 480, + 525 + ], + "spans": [ + { + "bbox": [ + 131, + 496, + 480, + 525 + ], + "score": 0.91, + "content": "\\gamma _ { i } ( { \\bf x } ) = \\frac { 1 } { \\sqrt { 2 L + 1 } } \\left( x _ { i } , \\frac { \\cos ( 2 ^ { 0 } \\pi { \\bf x } _ { i } ) } { 2 ^ { 0 } \\pi } , \\frac { \\sin ( 2 ^ { 0 } \\pi { \\bf x } _ { i } ) } { 2 ^ { 0 } \\pi } , \\ldots , \\frac { \\cos ( 2 ^ { L } \\pi { \\bf x } _ { i } ) } { 2 ^ { L } \\pi } , \\frac { \\sin ( 2 ^ { L } \\pi { \\bf x } _ { i } ) } { 2 ^ { L } \\pi } \\right) .", + "type": "interline_equation", + "image_path": "115f0ef27b3ae276645a06d8c15371d771109c767a72d8ffc95998a6ec1d55db.jpg" + } + ] + } + ], + "index": 40, + "virtual_lines": [ + { + "bbox": [ + 131, + 496, + 480, + 505.6666666666667 + ], + "spans": [], + "index": 39 + }, + { + "bbox": [ + 131, + 505.6666666666667, + 480, + 515.3333333333334 + ], + "spans": [], + "index": 40 + }, + { + "bbox": [ + 131, + 515.3333333333334, + 480, + 525.0 + ], + "spans": [], + "index": 41 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 532, + 505, + 563 + ], + "lines": [ + { + "bbox": [ + 106, + 532, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 532, + 505, + 546 + ], + "score": 1.0, + "content": "We will apply such encoding to each of the dimensions of the input coordinate for the body of the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 102, + 542, + 394, + 566 + ], + "spans": [ + { + "bbox": [ + 102, + 542, + 209, + 566 + ], + "score": 1.0, + "content": "invertible residual block:", + "type": "text" + }, + { + "bbox": [ + 209, + 543, + 389, + 564 + ], + "score": 0.93, + "content": "\\begin{array} { r } { \\bar { R _ { \\theta } } ( \\mathbf { x } ) = \\mathbf { x } + g _ { \\theta } \\left( \\frac { 1 } { \\sqrt { d } } [ \\gamma _ { 1 } \\left( \\mathbf { x } \\right) , \\mathbf { \\Omega } , \\mathbf { \\Omega } . . . , \\gamma _ { d } \\left( \\mathbf { \\bar { x } } \\right) ] \\right) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 542, + 394, + 566 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5, + "bbox_fs": [ + 102, + 532, + 505, + 566 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 578, + 336, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 578, + 338, + 590 + ], + "spans": [ + { + "bbox": [ + 106, + 578, + 338, + 590 + ], + "score": 1.0, + "content": "Ablation. We conduct ablation studies on two architec-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 589, + 337, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 589, + 337, + 601 + ], + "score": 1.0, + "content": "ture choices: invertibility and positional encoding. In", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 600, + 336, + 612 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 336, + 612 + ], + "score": 1.0, + "content": "this experiment, we deform a neural field representing the", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 610, + 337, + 622 + ], + "spans": [ + { + "bbox": [ + 106, + 610, + 337, + 622 + ], + "score": 1.0, + "content": "SDF of a 2D rectangle. We optimize each ablation case", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 621, + 337, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 337, + 635 + ], + "score": 1.0, + "content": "to satisfies the user specified constraints with following", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 628, + 340, + 652 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 129, + 646 + ], + "score": 1.0, + "content": "loss:", + "type": "text" + }, + { + "bbox": [ + 130, + 633, + 229, + 647 + ], + "score": 0.91, + "content": "\\begin{array} { r } { \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\left\\| D _ { \\theta } ( \\mathbf { h } _ { i } ) - \\mathbf { t } _ { i } \\right\\| ^ { 2 } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 230, + 628, + 340, + 652 + ], + "score": 1.0, + "content": ". The results are shown in", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 645, + 337, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 645, + 337, + 657 + ], + "score": 1.0, + "content": "Figure 4. If we replace the invertible architecture with", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 656, + 337, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 337, + 668 + ], + "score": 1.0, + "content": "SIREN as done in Deng et al. [25], the deformation field", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 667, + 337, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 337, + 679 + ], + "score": 1.0, + "content": "will tend to break topology (No inverse). 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This shows that our network architecture prioritizes", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 105, + 709, + 285, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 285, + 724 + ], + "score": 1.0, + "content": "natural deformation that preserves topology.", + "type": "text" + } + ], + "index": 56 + } + ], + "index": 50, + "bbox_fs": [ + 105, + 578, + 340, + 724 + ] + }, + { + "type": "image", + "bbox": [ + 344, + 580, + 495, + 648 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 344, + 580, + 495, + 648 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 344, + 580, + 495, + 648 + ], + "spans": [ + { + "bbox": [ + 344, + 580, + 495, + 648 + ], + "score": 0.958, + "type": "image", + "image_path": "513a5400ffef192f910dfe03539db2c361a75645844fec54771cf23c63e7d2b7.jpg" + } + ] + } + ], + "index": 57.5, + "virtual_lines": [ + { + "bbox": [ + 344, + 580, + 495, + 614.0 + ], + "spans": [], + "index": 57 + }, + { + "bbox": [ + 344, + 614.0, + 495, + 648.0 + ], + "spans": [], + "index": 58 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 344, + 659, + 505, + 693 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 343, + 659, + 505, + 670 + ], + "spans": [ + { + "bbox": [ + 343, + 659, + 505, + 670 + ], + "score": 1.0, + "content": "Figure 4: Architecture ablation on 2D", + "type": "text" + } + ], + "index": 59 + }, + { + "bbox": [ + 344, + 669, + 506, + 682 + ], + "spans": [ + { + "bbox": [ + 344, + 669, + 506, + 682 + ], + "score": 1.0, + "content": "SDF deformation. Blue points are han-", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 343, + 680, + 457, + 693 + ], + "spans": [ + { + "bbox": [ + 343, + 680, + 457, + 693 + ], + "score": 1.0, + "content": "dles; Red points are targets.", + "type": "text" + } + ], + "index": 61 + } + ], + "index": 60 + } + ], + "index": 58.75 + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 72, + 233, + 84 + ], + "lines": [ + { + "bbox": [ + 105, + 70, + 234, + 87 + ], + "spans": [ + { + "bbox": [ + 105, + 70, + 234, + 87 + ], + "score": 1.0, + "content": "5.3 Implicit Thin Shell Loss", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 92, + 506, + 159 + ], + "lines": [ + { + "bbox": [ + 106, + 92, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 92, + 315, + 105 + ], + "score": 1.0, + "content": "At this point, we have obtained the correspondences", + "type": "text" + }, + { + "bbox": [ + 315, + 92, + 362, + 104 + ], + "score": 0.92, + "content": "\\mathbf { y } = D _ { \\theta } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 92, + 386, + 105 + ], + "score": 1.0, + "content": ", with", + "type": "text" + }, + { + "bbox": [ + 387, + 94, + 394, + 103 + ], + "score": 0.46, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 395, + 92, + 505, + 105 + ], + "score": 1.0, + "content": "in the output (or deformed)", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 103, + 505, + 116 + ], + "spans": [ + { + "bbox": [ + 106, + 103, + 338, + 116 + ], + "score": 1.0, + "content": "space and y in the input space. Our next step is to design", + "type": "text" + }, + { + "bbox": [ + 339, + 104, + 362, + 116 + ], + "score": 0.91, + "content": "\\mathcal { L } _ { d f m }", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 103, + 505, + 116 + ], + "score": 1.0, + "content": "that compares these corresponding", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 114, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 114, + 506, + 127 + ], + "score": 1.0, + "content": "patches to ensure natural deformation. Recall that one way to ensure a natural-looking deformation is", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 126, + 506, + 137 + ], + "spans": [ + { + "bbox": [ + 106, + 126, + 506, + 137 + ], + "score": 1.0, + "content": "to minimize the amount the resistance to bending or stretching that happened during the deforma-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 136, + 506, + 149 + ], + "spans": [ + { + "bbox": [ + 105, + 136, + 506, + 149 + ], + "score": 1.0, + "content": "tion [1, 70]. We will develop novel loss functions for measuring stretching and bending. Please refer", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 146, + 427, + 161 + ], + "spans": [ + { + "bbox": [ + 104, + 146, + 427, + 161 + ], + "score": 1.0, + "content": "to the supplement for the connection between our loss and the thin shell energy.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3.5 + }, + { + "type": "title", + "bbox": [ + 107, + 170, + 204, + 182 + ], + "lines": [ + { + "bbox": [ + 105, + 168, + 205, + 184 + ], + "spans": [ + { + "bbox": [ + 105, + 168, + 205, + 184 + ], + "score": 1.0, + "content": "5.3.1 Stretching Loss", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 188, + 505, + 233 + ], + "lines": [ + { + "bbox": [ + 106, + 189, + 504, + 201 + ], + "spans": [ + { + "bbox": [ + 106, + 189, + 504, + 201 + ], + "score": 1.0, + "content": "Stretching can be captured by the change of dot product in tangent space. Intuitively, a local surface", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 200, + 506, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 506, + 212 + ], + "score": 1.0, + "content": "patch is stretched when the lengths of some tangent vectors change. The change of tangent vectors’", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 212, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 212, + 505, + 222 + ], + "score": 1.0, + "content": "norm can be measured by the tangent dot-product. With this said, the amount of stretch can be", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 222, + 298, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 298, + 233 + ], + "score": 1.0, + "content": "measured by the change of tangent dot product.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 106, + 237, + 505, + 304 + ], + "lines": [ + { + "bbox": [ + 105, + 237, + 505, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 505, + 250 + ], + "score": 1.0, + "content": "Note that we do not have access to analytical surface parameterization, so we need to express the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 248, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 106, + 248, + 506, + 261 + ], + "score": 1.0, + "content": "tangent dot product with neural fields and its derivative. We can describe the tangent dot product to", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 259, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 397, + 273 + ], + "score": 1.0, + "content": "the spatial dot product using the projection matrix. The tangent vector of", + "type": "text" + }, + { + "bbox": [ + 398, + 262, + 406, + 270 + ], + "score": 0.53, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 259, + 505, + 273 + ], + "score": 1.0, + "content": "can be parameterized by", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 271, + 505, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 182, + 283 + ], + "score": 1.0, + "content": "projecting a vector", + "type": "text" + }, + { + "bbox": [ + 183, + 273, + 190, + 281 + ], + "score": 0.51, + "content": "\\mathbf { v }", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 271, + 419, + 283 + ], + "score": 1.0, + "content": "to the tangent space. To achieve that, we need to multiply", + "type": "text" + }, + { + "bbox": [ + 420, + 273, + 427, + 281 + ], + "score": 0.27, + "content": "\\mathbf { v }", + "type": "inline_equation" + }, + { + "bbox": [ + 428, + 271, + 505, + 283 + ], + "score": 1.0, + "content": "with the projection", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 280, + 504, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 136, + 294 + ], + "score": 1.0, + "content": "matrix", + "type": "text" + }, + { + "bbox": [ + 136, + 281, + 267, + 294 + ], + "score": 0.91, + "content": "\\bar { \\mathbf { P } _ { G _ { \\theta } } } ( \\mathbf { x } ) = \\mathbf { I } - \\mathbf { n } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { \\bar { n } } _ { G _ { \\theta } } ( \\mathbf { \\bar { x } } ) ^ { T }", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 280, + 298, + 294 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 298, + 282, + 330, + 294 + ], + "score": 0.92, + "content": "\\mathbf { n } _ { G _ { \\theta } } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 280, + 452, + 294 + ], + "score": 1.0, + "content": "is the surface normal of point", + "type": "text" + }, + { + "bbox": [ + 452, + 283, + 460, + 292 + ], + "score": 0.46, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 280, + 464, + 294 + ], + "score": 1.0, + "content": ".", + "type": "text" + }, + { + "bbox": [ + 464, + 281, + 504, + 294 + ], + "score": 0.92, + "content": "\\mathbf { \\bar { P } } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v }", + "type": "inline_equation" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 293, + 284, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 293, + 273, + 304 + ], + "score": 1.0, + "content": "is a tangent vector in the tangent plane of", + "type": "text" + }, + { + "bbox": [ + 273, + 295, + 280, + 302 + ], + "score": 0.62, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 293, + 284, + 304 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14.5 + }, + { + "type": "text", + "bbox": [ + 106, + 308, + 505, + 364 + ], + "lines": [ + { + "bbox": [ + 105, + 308, + 505, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 396, + 322 + ], + "score": 1.0, + "content": "Now we are ready to compute the change of tangent dot-product. Let", + "type": "text" + }, + { + "bbox": [ + 397, + 310, + 406, + 320 + ], + "score": 0.87, + "content": "\\mathbf { t } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 308, + 425, + 322 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 425, + 310, + 435, + 321 + ], + "score": 0.88, + "content": "\\mathbf { t } _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 435, + 308, + 505, + 322 + ], + "score": 1.0, + "content": "be two arbitrary", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 320, + 505, + 332 + ], + "spans": [ + { + "bbox": [ + 106, + 320, + 218, + 332 + ], + "score": 1.0, + "content": "tangent vectors near point", + "type": "text" + }, + { + "bbox": [ + 219, + 322, + 227, + 330 + ], + "score": 0.61, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 227, + 320, + 505, + 332 + ], + "score": 1.0, + "content": "at the deformed shape. Further assume that these vectors can be", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 331, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 175, + 344 + ], + "score": 1.0, + "content": "parameterized as", + "type": "text" + }, + { + "bbox": [ + 176, + 331, + 240, + 343 + ], + "score": 0.91, + "content": "\\mathbf { t } _ { i } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 331, + 258, + 344 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 259, + 331, + 325, + 343 + ], + "score": 0.92, + "content": "\\mathbf { t } _ { j } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 331, + 505, + 344 + ], + "score": 1.0, + "content": ". These tangent vector will be transformed by", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 107, + 340, + 507, + 356 + ], + "spans": [ + { + "bbox": [ + 107, + 342, + 120, + 353 + ], + "score": 0.88, + "content": "D _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 121, + 340, + 140, + 356 + ], + "score": 1.0, + "content": "into", + "type": "text" + }, + { + "bbox": [ + 140, + 342, + 200, + 354 + ], + "score": 0.92, + "content": "\\mathbf { t } _ { i } ^ { \\prime } = \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { t } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 340, + 219, + 356 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 219, + 342, + 281, + 354 + ], + "score": 0.91, + "content": "\\mathbf { t } _ { j } ^ { \\prime } = \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { \\bar { x } } ) \\mathbf { t } _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 340, + 423, + 356 + ], + "score": 1.0, + "content": ". These are tangent vectors at point", + "type": "text" + }, + { + "bbox": [ + 423, + 344, + 430, + 353 + ], + "score": 0.38, + "content": "\\mathbf { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 431, + 340, + 507, + 356 + ], + "score": 1.0, + "content": "at the input shape.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 352, + 495, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 495, + 366 + ], + "score": 1.0, + "content": "The change of tangent dot-product with respect to these two vectors can be computed as follows:", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20 + }, + { + "type": "interline_equation", + "bbox": [ + 166, + 369, + 444, + 385 + ], + "lines": [ + { + "bbox": [ + 166, + 369, + 444, + 385 + ], + "spans": [ + { + "bbox": [ + 166, + 369, + 444, + 385 + ], + "score": 0.91, + "content": "\\begin{array} { r } { \\vert \\mathbf { t } _ { 1 } ^ { T } \\mathbf { t } _ { 2 } - \\mathbf { t } _ { 1 } ^ { \\prime T } \\mathbf { t } _ { 2 } ^ { \\prime } \\vert = \\vert \\mathbf { v } _ { 1 } ^ { T } \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) ^ { T } \\left( \\mathbf { I } - \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) ^ { T } \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\right) \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { 2 } \\vert . } \\end{array}", + "type": "interline_equation", + "image_path": "55ae1d4778cf1a5b605b4f6ba8167ec34cdc7a7d659dad5a3652492fa3cd586b.jpg" + } + ] + } + ], + "index": 23, + "virtual_lines": [ + { + "bbox": [ + 166, + 369, + 444, + 385 + ], + "spans": [], + "index": 23 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 389, + 506, + 423 + ], + "lines": [ + { + "bbox": [ + 104, + 387, + 507, + 402 + ], + "spans": [ + { + "bbox": [ + 104, + 387, + 507, + 402 + ], + "score": 1.0, + "content": "To minimize the stretch, we need to enforce that dot-product stays the same for all tangent vectors.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 102, + 395, + 509, + 418 + ], + "spans": [ + { + "bbox": [ + 102, + 395, + 318, + 418 + ], + "score": 1.0, + "content": "This can be done by minimize the matrix norm of", + "type": "text" + }, + { + "bbox": [ + 319, + 399, + 420, + 413 + ], + "score": 0.91, + "content": "\\mathbf { \\dot { P } } _ { G _ { \\theta } } ^ { T } \\bigl ( \\mathbf { I } - \\mathbf { \\dot { J } } _ { D _ { \\theta } } ^ { T } \\mathbf { J } _ { D _ { \\theta } } \\bigr ) \\mathbf { P } _ { G _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 420, + 395, + 509, + 418 + ], + "score": 1.0, + "content": ". Here, we drop the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 411, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 106, + 411, + 185, + 423 + ], + "score": 1.0, + "content": "function arguments", + "type": "text" + }, + { + "bbox": [ + 185, + 413, + 192, + 421 + ], + "score": 0.75, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 411, + 506, + 423 + ], + "score": 1.0, + "content": "for the matrix for notation clarity. With these, we define the the stretch loss as:", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25 + }, + { + "type": "interline_equation", + "bbox": [ + 196, + 426, + 414, + 456 + ], + "lines": [ + { + "bbox": [ + 196, + 426, + 414, + 456 + ], + "spans": [ + { + "bbox": [ + 196, + 426, + 414, + 456 + ], + "score": 0.92, + "content": "\\mathcal { L } _ { s } ( G _ { \\theta } ) = \\int _ { \\mathbf { x } \\in \\mathcal { M } _ { G _ { \\theta } } } \\left. \\mathbf { P } _ { G _ { \\theta } } ^ { T } \\left( \\mathbf { I } - \\mathbf { J } _ { D _ { \\theta } } ^ { T } \\mathbf { J } _ { D _ { \\theta } } \\right) \\mathbf { P } _ { G _ { \\theta } } \\right. _ { F } ^ { 2 } d \\mathbf { x } .", + "type": "interline_equation", + "image_path": "17478aacfa0825c24d4efefdcc10b097ca24f3d4fdf4bc8e89046ebe7f0b15a8.jpg" + } + ] + } + ], + "index": 27.5, + "virtual_lines": [ + { + "bbox": [ + 196, + 426, + 414, + 441.0 + ], + "spans": [], + "index": 27 + }, + { + "bbox": [ + 196, + 441.0, + 414, + 456.0 + ], + "spans": [], + "index": 28 + } + ] + }, + { + "type": "title", + "bbox": [ + 106, + 465, + 196, + 478 + ], + "lines": [ + { + "bbox": [ + 105, + 464, + 198, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 198, + 480 + ], + "score": 1.0, + "content": "5.3.2 Bending Loss", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 106, + 484, + 505, + 574 + ], + "lines": [ + { + "bbox": [ + 105, + 484, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 506, + 497 + ], + "score": 1.0, + "content": "Bending can be characterized by the change of surface curvature (e.g., making the surface more or", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 496, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 505, + 507 + ], + "score": 1.0, + "content": "less curved). Intuitively, curvature can be described as the change of tangent dot product along the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 505, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 260, + 520 + ], + "score": 1.0, + "content": "surface normal direction [16, 59]. Let", + "type": "text" + }, + { + "bbox": [ + 261, + 506, + 326, + 518 + ], + "score": 0.93, + "content": "\\mathbf { t } _ { 1 } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 505, + 344, + 520 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 345, + 506, + 411, + 518 + ], + "score": 0.92, + "content": "\\mathbf { t } _ { 2 } = \\mathbf { \\bar { P } } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { \\bar { v } } _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 505, + 506, + 520 + ], + "score": 1.0, + "content": "be two tangent vectors", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 518, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 518, + 116, + 529 + ], + "score": 1.0, + "content": "at", + "type": "text" + }, + { + "bbox": [ + 116, + 519, + 123, + 527 + ], + "score": 0.43, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 124, + 518, + 345, + 529 + ], + "score": 1.0, + "content": ". Consider the tangent dot product of the surface family", + "type": "text" + }, + { + "bbox": [ + 346, + 518, + 389, + 529 + ], + "score": 0.9, + "content": "\\mathbf { x } + t \\mathbf { n } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 518, + 505, + 529 + ], + "score": 1.0, + "content": ". Note that this set of surface", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 228, + 541 + ], + "score": 1.0, + "content": "corresponding to the level sets", + "type": "text" + }, + { + "bbox": [ + 228, + 528, + 291, + 540 + ], + "score": 0.92, + "content": "{ \\bf \\dot { \\{ p \\vert } } G _ { \\theta } ( { \\bf p } ) = t \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 528, + 300, + 541 + ], + "score": 1.0, + "content": "if", + "type": "text" + }, + { + "bbox": [ + 301, + 528, + 314, + 539 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 315, + 528, + 505, + 541 + ], + "score": 1.0, + "content": "is approximating an SDF [54]. Then the change", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 538, + 510, + 575 + ], + "spans": [ + { + "bbox": [ + 104, + 538, + 507, + 552 + ], + "score": 1.0, + "content": "of dot product along the surface normal direction can be given by Hessian and directional derivative:", + "type": "text" + }, + { + "bbox": [ + 107, + 550, + 219, + 564 + ], + "score": 0.92, + "content": "\\begin{array} { r } { \\frac { d } { d t } \\mathbf { t } _ { 1 } ^ { T } \\mathbf { t } _ { 2 } \\mathbf { \\bar { \\Psi } } _ { t = 0 } = \\mathbf { t } _ { 1 } ^ { T } \\bar { H _ { G _ { \\theta } } } ( \\mathbf { x } ) \\mathbf { t } _ { 2 } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 543, + 510, + 575 + ], + "score": 1.0, + "content": ". Intuitively, the larger this value is, the faster the surface changes whenmal direction, which means the surface has larger curvature.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32.5 + }, + { + "type": "text", + "bbox": [ + 106, + 578, + 505, + 657 + ], + "lines": [ + { + "bbox": [ + 105, + 577, + 505, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 505, + 591 + ], + "score": 1.0, + "content": "Measuring bending amounts to measure the change of tangent dot-product derivative along the surface", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 588, + 504, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 439, + 603 + ], + "score": 1.0, + "content": "normal direction. Similar to the previous section, assume we have tangent vectors", + "type": "text" + }, + { + "bbox": [ + 440, + 589, + 504, + 601 + ], + "score": 0.92, + "content": "\\mathbf { t } _ { i } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { i }", + "type": "inline_equation" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 600, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 123, + 613 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 124, + 600, + 189, + 612 + ], + "score": 0.91, + "content": "\\mathbf { t } _ { j } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 600, + 505, + 613 + ], + "score": 1.0, + "content": ". These tangent vectors are are transformed by the Jacobian of the deformation", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 610, + 506, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 127, + 624 + ], + "score": 1.0, + "content": "field", + "type": "text" + }, + { + "bbox": [ + 127, + 612, + 159, + 623 + ], + "score": 0.88, + "content": "\\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 610, + 172, + 624 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 172, + 611, + 235, + 623 + ], + "score": 0.94, + "content": "\\dot { \\mathbf { t } } _ { i } ^ { \\prime } = \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { t } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 610, + 254, + 624 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 254, + 611, + 319, + 624 + ], + "score": 0.92, + "content": "\\mathbf { t } _ { j } ^ { \\prime } = \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { t } _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 319, + 610, + 350, + 624 + ], + "score": 1.0, + "content": ". Since", + "type": "text" + }, + { + "bbox": [ + 350, + 611, + 360, + 623 + ], + "score": 0.88, + "content": "\\mathbf { t } _ { i } ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 610, + 379, + 624 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 379, + 611, + 389, + 624 + ], + "score": 0.86, + "content": "\\mathbf { t } _ { j } ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 610, + 506, + 624 + ], + "score": 1.0, + "content": "are tangent vectors at point", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 621, + 506, + 634 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 114, + 633 + ], + "score": 0.44, + "content": "\\mathbf { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 621, + 174, + 634 + ], + "score": 1.0, + "content": "on the surface", + "type": "text" + }, + { + "bbox": [ + 175, + 623, + 194, + 633 + ], + "score": 0.86, + "content": "\\mathcal { M } _ { F }", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 621, + 506, + 634 + ], + "score": 1.0, + "content": ", the derivative of tangent dot-product is given by the hessian matrix of field", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 107, + 628, + 509, + 652 + ], + "spans": [ + { + "bbox": [ + 107, + 634, + 115, + 644 + ], + "score": 0.47, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 633, + 398, + 647 + ], + "score": 0.81, + "content": ": \\mathbf { \\Gamma } _ { d t } ^ { d } \\mathbf { t } _ { 1 } ^ { \\prime T } \\mathbf { t } _ { 2 } ^ { \\prime } | _ { t = 0 } = \\mathbf { t } _ { 1 } ^ { \\prime T } H _ { F } ( D _ { \\theta } ( \\mathbf { x } ) ) \\mathbf { t } _ { 2 } ^ { \\prime } = \\mathbf { t } _ { 1 } ^ { T } \\mathbf { J } _ { D _ { \\theta } } ^ { T } ( \\mathbf { x } ) H _ { F } ( D _ { \\theta } ( \\mathbf { x } ) ) \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { t } _ { 2 } .", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 628, + 509, + 652 + ], + "score": 1.0, + "content": ". We will drop the function", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 645, + 507, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 645, + 155, + 658 + ], + "score": 1.0, + "content": "argument to", + "type": "text" + }, + { + "bbox": [ + 156, + 646, + 173, + 657 + ], + "score": 0.78, + "content": "\\mathbf { J } _ { D _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 645, + 177, + 658 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 177, + 646, + 197, + 657 + ], + "score": 0.66, + "content": "H _ { G _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 197, + 645, + 218, + 658 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 218, + 646, + 237, + 657 + ], + "score": 0.9, + "content": "\\mathbf { P } _ { G _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 645, + 507, + 658 + ], + "score": 1.0, + "content": "for notation clarity. 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We will", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 46.5 + } + ], + "page_idx": 6, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 741, + 308, + 750 + ], + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 752 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 752 + ], + "score": 1.0, + "content": "7", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 72, + 233, + 84 + ], + "lines": [ + { + "bbox": [ + 105, + 70, + 234, + 87 + ], + "spans": [ + { + "bbox": [ + 105, + 70, + 234, + 87 + ], + "score": 1.0, + "content": "5.3 Implicit Thin Shell Loss", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 92, + 506, + 159 + ], + "lines": [ + { + "bbox": [ + 106, + 92, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 92, + 315, + 105 + ], + "score": 1.0, + "content": "At this point, we have obtained the correspondences", + "type": "text" + }, + { + "bbox": [ + 315, + 92, + 362, + 104 + ], + "score": 0.92, + "content": "\\mathbf { y } = D _ { \\theta } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 92, + 386, + 105 + ], + "score": 1.0, + "content": ", with", + "type": "text" + }, + { + "bbox": [ + 387, + 94, + 394, + 103 + ], + "score": 0.46, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 395, + 92, + 505, + 105 + ], + "score": 1.0, + "content": "in the output (or deformed)", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 103, + 505, + 116 + ], + "spans": [ + { + "bbox": [ + 106, + 103, + 338, + 116 + ], + "score": 1.0, + "content": "space and y in the input space. Our next step is to design", + "type": "text" + }, + { + "bbox": [ + 339, + 104, + 362, + 116 + ], + "score": 0.91, + "content": "\\mathcal { L } _ { d f m }", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 103, + 505, + 116 + ], + "score": 1.0, + "content": "that compares these corresponding", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 114, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 114, + 506, + 127 + ], + "score": 1.0, + "content": "patches to ensure natural deformation. Recall that one way to ensure a natural-looking deformation is", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 126, + 506, + 137 + ], + "spans": [ + { + "bbox": [ + 106, + 126, + 506, + 137 + ], + "score": 1.0, + "content": "to minimize the amount the resistance to bending or stretching that happened during the deforma-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 136, + 506, + 149 + ], + "spans": [ + { + "bbox": [ + 105, + 136, + 506, + 149 + ], + "score": 1.0, + "content": "tion [1, 70]. We will develop novel loss functions for measuring stretching and bending. Please refer", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 146, + 427, + 161 + ], + "spans": [ + { + "bbox": [ + 104, + 146, + 427, + 161 + ], + "score": 1.0, + "content": "to the supplement for the connection between our loss and the thin shell energy.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3.5, + "bbox_fs": [ + 104, + 92, + 506, + 161 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 170, + 204, + 182 + ], + "lines": [ + { + "bbox": [ + 105, + 168, + 205, + 184 + ], + "spans": [ + { + "bbox": [ + 105, + 168, + 205, + 184 + ], + "score": 1.0, + "content": "5.3.1 Stretching Loss", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 188, + 505, + 233 + ], + "lines": [ + { + "bbox": [ + 106, + 189, + 504, + 201 + ], + "spans": [ + { + "bbox": [ + 106, + 189, + 504, + 201 + ], + "score": 1.0, + "content": "Stretching can be captured by the change of dot product in tangent space. Intuitively, a local surface", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 200, + 506, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 506, + 212 + ], + "score": 1.0, + "content": "patch is stretched when the lengths of some tangent vectors change. The change of tangent vectors’", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 212, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 212, + 505, + 222 + ], + "score": 1.0, + "content": "norm can be measured by the tangent dot-product. With this said, the amount of stretch can be", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 222, + 298, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 298, + 233 + ], + "score": 1.0, + "content": "measured by the change of tangent dot product.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9.5, + "bbox_fs": [ + 105, + 189, + 506, + 233 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 237, + 505, + 304 + ], + "lines": [ + { + "bbox": [ + 105, + 237, + 505, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 505, + 250 + ], + "score": 1.0, + "content": "Note that we do not have access to analytical surface parameterization, so we need to express the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 248, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 106, + 248, + 506, + 261 + ], + "score": 1.0, + "content": "tangent dot product with neural fields and its derivative. We can describe the tangent dot product to", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 259, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 397, + 273 + ], + "score": 1.0, + "content": "the spatial dot product using the projection matrix. The tangent vector of", + "type": "text" + }, + { + "bbox": [ + 398, + 262, + 406, + 270 + ], + "score": 0.53, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 259, + 505, + 273 + ], + "score": 1.0, + "content": "can be parameterized by", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 271, + 505, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 182, + 283 + ], + "score": 1.0, + "content": "projecting a vector", + "type": "text" + }, + { + "bbox": [ + 183, + 273, + 190, + 281 + ], + "score": 0.51, + "content": "\\mathbf { v }", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 271, + 419, + 283 + ], + "score": 1.0, + "content": "to the tangent space. To achieve that, we need to multiply", + "type": "text" + }, + { + "bbox": [ + 420, + 273, + 427, + 281 + ], + "score": 0.27, + "content": "\\mathbf { v }", + "type": "inline_equation" + }, + { + "bbox": [ + 428, + 271, + 505, + 283 + ], + "score": 1.0, + "content": "with the projection", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 280, + 504, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 136, + 294 + ], + "score": 1.0, + "content": "matrix", + "type": "text" + }, + { + "bbox": [ + 136, + 281, + 267, + 294 + ], + "score": 0.91, + "content": "\\bar { \\mathbf { P } _ { G _ { \\theta } } } ( \\mathbf { x } ) = \\mathbf { I } - \\mathbf { n } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { \\bar { n } } _ { G _ { \\theta } } ( \\mathbf { \\bar { x } } ) ^ { T }", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 280, + 298, + 294 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 298, + 282, + 330, + 294 + ], + "score": 0.92, + "content": "\\mathbf { n } _ { G _ { \\theta } } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 280, + 452, + 294 + ], + "score": 1.0, + "content": "is the surface normal of point", + "type": "text" + }, + { + "bbox": [ + 452, + 283, + 460, + 292 + ], + "score": 0.46, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 280, + 464, + 294 + ], + "score": 1.0, + "content": ".", + "type": "text" + }, + { + "bbox": [ + 464, + 281, + 504, + 294 + ], + "score": 0.92, + "content": "\\mathbf { \\bar { P } } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v }", + "type": "inline_equation" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 293, + 284, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 293, + 273, + 304 + ], + "score": 1.0, + "content": "is a tangent vector in the tangent plane of", + "type": "text" + }, + { + "bbox": [ + 273, + 295, + 280, + 302 + ], + "score": 0.62, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 293, + 284, + 304 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14.5, + "bbox_fs": [ + 105, + 237, + 506, + 304 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 308, + 505, + 364 + ], + "lines": [ + { + "bbox": [ + 105, + 308, + 505, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 396, + 322 + ], + "score": 1.0, + "content": "Now we are ready to compute the change of tangent dot-product. Let", + "type": "text" + }, + { + "bbox": [ + 397, + 310, + 406, + 320 + ], + "score": 0.87, + "content": "\\mathbf { t } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 308, + 425, + 322 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 425, + 310, + 435, + 321 + ], + "score": 0.88, + "content": "\\mathbf { t } _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 435, + 308, + 505, + 322 + ], + "score": 1.0, + "content": "be two arbitrary", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 320, + 505, + 332 + ], + "spans": [ + { + "bbox": [ + 106, + 320, + 218, + 332 + ], + "score": 1.0, + "content": "tangent vectors near point", + "type": "text" + }, + { + "bbox": [ + 219, + 322, + 227, + 330 + ], + "score": 0.61, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 227, + 320, + 505, + 332 + ], + "score": 1.0, + "content": "at the deformed shape. Further assume that these vectors can be", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 331, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 175, + 344 + ], + "score": 1.0, + "content": "parameterized as", + "type": "text" + }, + { + "bbox": [ + 176, + 331, + 240, + 343 + ], + "score": 0.91, + "content": "\\mathbf { t } _ { i } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 331, + 258, + 344 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 259, + 331, + 325, + 343 + ], + "score": 0.92, + "content": "\\mathbf { t } _ { j } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 331, + 505, + 344 + ], + "score": 1.0, + "content": ". These tangent vector will be transformed by", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 107, + 340, + 507, + 356 + ], + "spans": [ + { + "bbox": [ + 107, + 342, + 120, + 353 + ], + "score": 0.88, + "content": "D _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 121, + 340, + 140, + 356 + ], + "score": 1.0, + "content": "into", + "type": "text" + }, + { + "bbox": [ + 140, + 342, + 200, + 354 + ], + "score": 0.92, + "content": "\\mathbf { t } _ { i } ^ { \\prime } = \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { t } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 340, + 219, + 356 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 219, + 342, + 281, + 354 + ], + "score": 0.91, + "content": "\\mathbf { t } _ { j } ^ { \\prime } = \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { \\bar { x } } ) \\mathbf { t } _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 340, + 423, + 356 + ], + "score": 1.0, + "content": ". These are tangent vectors at point", + "type": "text" + }, + { + "bbox": [ + 423, + 344, + 430, + 353 + ], + "score": 0.38, + "content": "\\mathbf { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 431, + 340, + 507, + 356 + ], + "score": 1.0, + "content": "at the input shape.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 352, + 495, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 495, + 366 + ], + "score": 1.0, + "content": "The change of tangent dot-product with respect to these two vectors can be computed as follows:", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20, + "bbox_fs": [ + 105, + 308, + 507, + 366 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 166, + 369, + 444, + 385 + ], + "lines": [ + { + "bbox": [ + 166, + 369, + 444, + 385 + ], + "spans": [ + { + "bbox": [ + 166, + 369, + 444, + 385 + ], + "score": 0.91, + "content": "\\begin{array} { r } { \\vert \\mathbf { t } _ { 1 } ^ { T } \\mathbf { t } _ { 2 } - \\mathbf { t } _ { 1 } ^ { \\prime T } \\mathbf { t } _ { 2 } ^ { \\prime } \\vert = \\vert \\mathbf { v } _ { 1 } ^ { T } \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) ^ { T } \\left( \\mathbf { I } - \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) ^ { T } \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\right) \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { 2 } \\vert . } \\end{array}", + "type": "interline_equation", + "image_path": "55ae1d4778cf1a5b605b4f6ba8167ec34cdc7a7d659dad5a3652492fa3cd586b.jpg" + } + ] + } + ], + "index": 23, + "virtual_lines": [ + { + "bbox": [ + 166, + 369, + 444, + 385 + ], + "spans": [], + "index": 23 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 389, + 506, + 423 + ], + "lines": [ + { + "bbox": [ + 104, + 387, + 507, + 402 + ], + "spans": [ + { + "bbox": [ + 104, + 387, + 507, + 402 + ], + "score": 1.0, + "content": "To minimize the stretch, we need to enforce that dot-product stays the same for all tangent vectors.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 102, + 395, + 509, + 418 + ], + "spans": [ + { + "bbox": [ + 102, + 395, + 318, + 418 + ], + "score": 1.0, + "content": "This can be done by minimize the matrix norm of", + "type": "text" + }, + { + "bbox": [ + 319, + 399, + 420, + 413 + ], + "score": 0.91, + "content": "\\mathbf { \\dot { P } } _ { G _ { \\theta } } ^ { T } \\bigl ( \\mathbf { I } - \\mathbf { \\dot { J } } _ { D _ { \\theta } } ^ { T } \\mathbf { J } _ { D _ { \\theta } } \\bigr ) \\mathbf { P } _ { G _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 420, + 395, + 509, + 418 + ], + "score": 1.0, + "content": ". Here, we drop the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 411, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 106, + 411, + 185, + 423 + ], + "score": 1.0, + "content": "function arguments", + "type": "text" + }, + { + "bbox": [ + 185, + 413, + 192, + 421 + ], + "score": 0.75, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 411, + 506, + 423 + ], + "score": 1.0, + "content": "for the matrix for notation clarity. With these, we define the the stretch loss as:", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25, + "bbox_fs": [ + 102, + 387, + 509, + 423 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 196, + 426, + 414, + 456 + ], + "lines": [ + { + "bbox": [ + 196, + 426, + 414, + 456 + ], + "spans": [ + { + "bbox": [ + 196, + 426, + 414, + 456 + ], + "score": 0.92, + "content": "\\mathcal { L } _ { s } ( G _ { \\theta } ) = \\int _ { \\mathbf { x } \\in \\mathcal { M } _ { G _ { \\theta } } } \\left. \\mathbf { P } _ { G _ { \\theta } } ^ { T } \\left( \\mathbf { I } - \\mathbf { J } _ { D _ { \\theta } } ^ { T } \\mathbf { J } _ { D _ { \\theta } } \\right) \\mathbf { P } _ { G _ { \\theta } } \\right. _ { F } ^ { 2 } d \\mathbf { x } .", + "type": "interline_equation", + "image_path": "17478aacfa0825c24d4efefdcc10b097ca24f3d4fdf4bc8e89046ebe7f0b15a8.jpg" + } + ] + } + ], + "index": 27.5, + "virtual_lines": [ + { + "bbox": [ + 196, + 426, + 414, + 441.0 + ], + "spans": [], + "index": 27 + }, + { + "bbox": [ + 196, + 441.0, + 414, + 456.0 + ], + "spans": [], + "index": 28 + } + ] + }, + { + "type": "title", + "bbox": [ + 106, + 465, + 196, + 478 + ], + "lines": [ + { + "bbox": [ + 105, + 464, + 198, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 198, + 480 + ], + "score": 1.0, + "content": "5.3.2 Bending Loss", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 106, + 484, + 505, + 574 + ], + "lines": [ + { + "bbox": [ + 105, + 484, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 506, + 497 + ], + "score": 1.0, + "content": "Bending can be characterized by the change of surface curvature (e.g., making the surface more or", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 496, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 505, + 507 + ], + "score": 1.0, + "content": "less curved). Intuitively, curvature can be described as the change of tangent dot product along the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 505, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 260, + 520 + ], + "score": 1.0, + "content": "surface normal direction [16, 59]. Let", + "type": "text" + }, + { + "bbox": [ + 261, + 506, + 326, + 518 + ], + "score": 0.93, + "content": "\\mathbf { t } _ { 1 } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 505, + 344, + 520 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 345, + 506, + 411, + 518 + ], + "score": 0.92, + "content": "\\mathbf { t } _ { 2 } = \\mathbf { \\bar { P } } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { \\bar { v } } _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 505, + 506, + 520 + ], + "score": 1.0, + "content": "be two tangent vectors", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 518, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 518, + 116, + 529 + ], + "score": 1.0, + "content": "at", + "type": "text" + }, + { + "bbox": [ + 116, + 519, + 123, + 527 + ], + "score": 0.43, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 124, + 518, + 345, + 529 + ], + "score": 1.0, + "content": ". Consider the tangent dot product of the surface family", + "type": "text" + }, + { + "bbox": [ + 346, + 518, + 389, + 529 + ], + "score": 0.9, + "content": "\\mathbf { x } + t \\mathbf { n } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 518, + 505, + 529 + ], + "score": 1.0, + "content": ". Note that this set of surface", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 228, + 541 + ], + "score": 1.0, + "content": "corresponding to the level sets", + "type": "text" + }, + { + "bbox": [ + 228, + 528, + 291, + 540 + ], + "score": 0.92, + "content": "{ \\bf \\dot { \\{ p \\vert } } G _ { \\theta } ( { \\bf p } ) = t \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 528, + 300, + 541 + ], + "score": 1.0, + "content": "if", + "type": "text" + }, + { + "bbox": [ + 301, + 528, + 314, + 539 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 315, + 528, + 505, + 541 + ], + "score": 1.0, + "content": "is approximating an SDF [54]. Then the change", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 538, + 510, + 575 + ], + "spans": [ + { + "bbox": [ + 104, + 538, + 507, + 552 + ], + "score": 1.0, + "content": "of dot product along the surface normal direction can be given by Hessian and directional derivative:", + "type": "text" + }, + { + "bbox": [ + 107, + 550, + 219, + 564 + ], + "score": 0.92, + "content": "\\begin{array} { r } { \\frac { d } { d t } \\mathbf { t } _ { 1 } ^ { T } \\mathbf { t } _ { 2 } \\mathbf { \\bar { \\Psi } } _ { t = 0 } = \\mathbf { t } _ { 1 } ^ { T } \\bar { H _ { G _ { \\theta } } } ( \\mathbf { x } ) \\mathbf { t } _ { 2 } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 543, + 510, + 575 + ], + "score": 1.0, + "content": ". Intuitively, the larger this value is, the faster the surface changes whenmal direction, which means the surface has larger curvature.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32.5, + "bbox_fs": [ + 104, + 484, + 510, + 575 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 578, + 505, + 657 + ], + "lines": [ + { + "bbox": [ + 105, + 577, + 505, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 505, + 591 + ], + "score": 1.0, + "content": "Measuring bending amounts to measure the change of tangent dot-product derivative along the surface", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 588, + 504, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 439, + 603 + ], + "score": 1.0, + "content": "normal direction. Similar to the previous section, assume we have tangent vectors", + "type": "text" + }, + { + "bbox": [ + 440, + 589, + 504, + 601 + ], + "score": 0.92, + "content": "\\mathbf { t } _ { i } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { i }", + "type": "inline_equation" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 600, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 123, + 613 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 124, + 600, + 189, + 612 + ], + "score": 0.91, + "content": "\\mathbf { t } _ { j } = \\mathbf { P } _ { G _ { \\theta } } ( \\mathbf { x } ) \\mathbf { v } _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 600, + 505, + 613 + ], + "score": 1.0, + "content": ". These tangent vectors are are transformed by the Jacobian of the deformation", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 610, + 506, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 127, + 624 + ], + "score": 1.0, + "content": "field", + "type": "text" + }, + { + "bbox": [ + 127, + 612, + 159, + 623 + ], + "score": 0.88, + "content": "\\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 610, + 172, + 624 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 172, + 611, + 235, + 623 + ], + "score": 0.94, + "content": "\\dot { \\mathbf { t } } _ { i } ^ { \\prime } = \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { t } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 610, + 254, + 624 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 254, + 611, + 319, + 624 + ], + "score": 0.92, + "content": "\\mathbf { t } _ { j } ^ { \\prime } = \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { t } _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 319, + 610, + 350, + 624 + ], + "score": 1.0, + "content": ". Since", + "type": "text" + }, + { + "bbox": [ + 350, + 611, + 360, + 623 + ], + "score": 0.88, + "content": "\\mathbf { t } _ { i } ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 610, + 379, + 624 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 379, + 611, + 389, + 624 + ], + "score": 0.86, + "content": "\\mathbf { t } _ { j } ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 610, + 506, + 624 + ], + "score": 1.0, + "content": "are tangent vectors at point", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 621, + 506, + 634 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 114, + 633 + ], + "score": 0.44, + "content": "\\mathbf { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 621, + 174, + 634 + ], + "score": 1.0, + "content": "on the surface", + "type": "text" + }, + { + "bbox": [ + 175, + 623, + 194, + 633 + ], + "score": 0.86, + "content": "\\mathcal { M } _ { F }", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 621, + 506, + 634 + ], + "score": 1.0, + "content": ", the derivative of tangent dot-product is given by the hessian matrix of field", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 107, + 628, + 509, + 652 + ], + "spans": [ + { + "bbox": [ + 107, + 634, + 115, + 644 + ], + "score": 0.47, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 633, + 398, + 647 + ], + "score": 0.81, + "content": ": \\mathbf { \\Gamma } _ { d t } ^ { d } \\mathbf { t } _ { 1 } ^ { \\prime T } \\mathbf { t } _ { 2 } ^ { \\prime } | _ { t = 0 } = \\mathbf { t } _ { 1 } ^ { \\prime T } H _ { F } ( D _ { \\theta } ( \\mathbf { x } ) ) \\mathbf { t } _ { 2 } ^ { \\prime } = \\mathbf { t } _ { 1 } ^ { T } \\mathbf { J } _ { D _ { \\theta } } ^ { T } ( \\mathbf { x } ) H _ { F } ( D _ { \\theta } ( \\mathbf { x } ) ) \\mathbf { J } _ { D _ { \\theta } } ( \\mathbf { x } ) \\mathbf { t } _ { 2 } .", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 628, + 509, + 652 + ], + "score": 1.0, + "content": ". We will drop the function", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 645, + 507, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 645, + 155, + 658 + ], + "score": 1.0, + "content": "argument to", + "type": "text" + }, + { + "bbox": [ + 156, + 646, + 173, + 657 + ], + "score": 0.78, + "content": "\\mathbf { J } _ { D _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 645, + 177, + 658 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 177, + 646, + 197, + 657 + ], + "score": 0.66, + "content": "H _ { G _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 197, + 645, + 218, + 658 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 218, + 646, + 237, + 657 + ], + "score": 0.9, + "content": "\\mathbf { P } _ { G _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 645, + 507, + 658 + ], + "score": 1.0, + "content": "for notation clarity. The change of tangent dot-product derivative is:", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 577, + 509, + 658 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 149, + 661, + 461, + 689 + ], + "lines": [ + { + "bbox": [ + 149, + 661, + 461, + 689 + ], + "spans": [ + { + "bbox": [ + 149, + 661, + 461, + 689 + ], + "score": 0.92, + "content": "\\left| \\frac { d } { d t } \\left( \\mathbf { t } _ { 1 } ^ { T } \\mathbf { t } _ { 2 } - \\mathbf { t } _ { 1 } ^ { \\prime T } \\mathbf { t } _ { 2 } ^ { \\prime } \\right) _ { t = 0 } \\right| = \\left| \\mathbf { v } _ { 1 } ^ { T } \\mathbf { P } _ { G _ { \\theta } } ^ { T } \\left( H _ { G _ { \\theta } } - \\mathbf { J } _ { D _ { \\theta } } ^ { T } H _ { F } ( D _ { \\theta } ( \\mathbf { x } ) ) \\mathbf { J } _ { D _ { \\theta } } \\right) \\mathbf { P } _ { G _ { \\theta } } \\mathbf { v } _ { 2 } \\right| .", + "type": "interline_equation", + "image_path": "be54971a5a60e73bdcd5debb0fd63cc7fee4f4a5f165a9cbfea5a89a4ff84aef.jpg" + } + ] + } + ], + "index": 44, + "virtual_lines": [ + { + "bbox": [ + 149, + 661, + 461, + 670.3333333333334 + ], + "spans": [], + "index": 43 + }, + { + "bbox": [ + 149, + 670.3333333333334, + 461, + 679.6666666666667 + ], + "spans": [], + "index": 44 + }, + { + "bbox": [ + 149, + 679.6666666666667, + 461, + 689.0000000000001 + ], + "spans": [], + "index": 45 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 698, + 505, + 724 + ], + "lines": [ + { + "bbox": [ + 105, + 697, + 504, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 697, + 445, + 712 + ], + "score": 1.0, + "content": "If there is almost no bending happened between the infinitesimal patches around", + "type": "text" + }, + { + "bbox": [ + 445, + 701, + 453, + 709 + ], + "score": 0.66, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 453, + 697, + 472, + 712 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 473, + 701, + 480, + 710 + ], + "score": 0.63, + "content": "\\mathbf { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 697, + 504, + 712 + ], + "score": 1.0, + "content": ", then", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 709, + 506, + 725 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 158, + 725 + ], + "score": 1.0, + "content": "the quantity", + "type": "text" + }, + { + "bbox": [ + 158, + 709, + 253, + 725 + ], + "score": 0.91, + "content": "\\begin{array} { r } { \\left| \\frac { d } { d t } \\left( \\mathbf { t } _ { 1 } ^ { T } \\mathbf { t } _ { 2 } - \\mathbf { t } _ { 1 } ^ { \\prime T } \\bar { \\mathbf { t } } _ { 2 } ^ { \\prime } \\right) _ { t = 0 } \\right| } \\end{array} \\qquad = 0 .", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 709, + 506, + 725 + ], + "score": 1.0, + "content": "should stay close to 0 for all pairs of tangent vectors. We will", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 46.5, + "bbox_fs": [ + 105, + 697, + 506, + 725 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 71, + 505, + 106 + ], + "lines": [ + { + "bbox": [ + 103, + 69, + 508, + 90 + ], + "spans": [ + { + "bbox": [ + 103, + 69, + 252, + 90 + ], + "score": 1.0, + "content": "quantify this by the matrix norm of", + "type": "text" + }, + { + "bbox": [ + 253, + 72, + 417, + 86 + ], + "score": 0.88, + "content": "{ \\bf P } _ { G _ { \\theta } } ^ { T } \\left( H _ { G _ { \\theta } } - { \\bf J } _ { D _ { \\theta } } ^ { T } H _ { F } ( D _ { \\theta } ( { \\bf x } ) ) { \\bf J } _ { D _ { \\theta } } \\right) { \\bf P } _ { G _ { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 69, + 508, + 90 + ], + "score": 1.0, + "content": ". 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We optimize", + "type": "text" + }, + { + "bbox": [ + 463, + 442, + 484, + 454 + ], + "score": 0.91, + "content": "\\mathcal { L } ( \\boldsymbol { \\theta } )", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 442, + 505, + 455 + ], + "score": 1.0, + "content": "with", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 453, + 491, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 453, + 274, + 465 + ], + "score": 1.0, + "content": "Adam optimizer to obtain the output field", + "type": "text" + }, + { + "bbox": [ + 274, + 453, + 288, + 464 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 288, + 453, + 491, + 465 + ], + "score": 1.0, + "content": ". Hyperparameters are provided in the supplement.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29 + }, + { + "type": "title", + "bbox": [ + 107, + 479, + 231, + 492 + ], + "lines": [ + { + "bbox": [ + 105, + 478, + 232, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 232, + 494 + ], + "score": 1.0, + "content": "6 Deformation Results", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 106, + 502, + 505, + 591 + ], + "lines": [ + { + "bbox": [ + 105, + 502, + 505, + 515 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 505, + 515 + ], + "score": 1.0, + "content": "In this section, we will demonstrate the results of our methods to shape deformation. The shapes", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 514, + 506, + 526 + ], + "spans": [ + { + "bbox": [ + 106, + 514, + 506, + 526 + ], + "score": 1.0, + "content": "for deformation are taken from Sorkine-Hornung and Alexa [70]. To create neural fields from these", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 525, + 505, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 505, + 537 + ], + "score": 1.0, + "content": "meshes, we follow the procedure of Park et al. [56] to compute ground-truth SDF for locations", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 535, + 506, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 172, + 548 + ], + "score": 1.0, + "content": "sampled within", + "type": "text" + }, + { + "bbox": [ + 172, + 535, + 204, + 547 + ], + "score": 0.92, + "content": "[ - 1 , 1 ] ^ { 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 535, + 506, + 548 + ], + "score": 1.0, + "content": ". We then fit a SIREN [66] to the ground-truth SDF to generate our initial", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 546, + 506, + 559 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 506, + 559 + ], + "score": 1.0, + "content": "neural fields. Our main baseline is ARAP [70, 86]. The simplest way to use ARAP to edit neural", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 556, + 506, + 570 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 506, + 570 + ], + "score": 1.0, + "content": "fields is applying it on a mesh extracted from the input neural fields using marching cubes [44, 45].", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 567, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 567, + 506, + 581 + ], + "score": 1.0, + "content": "We first present results comparing with ARAP applied to the extracted mesh. Then we will conduct", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 580, + 351, + 591 + ], + "spans": [ + { + "bbox": [ + 106, + 580, + 351, + 591 + ], + "score": 1.0, + "content": "an analysis to show our losses encourage the right behaviors.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 35.5 + }, + { + "type": "text", + "bbox": [ + 106, + 601, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 601, + 505, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 601, + 505, + 614 + ], + "score": 1.0, + "content": "Comparing to ARAP baseline. We follow ARAP [70] to create a set of basic shape deformation", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 613, + 505, + 625 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 505, + 625 + ], + "score": 1.0, + "content": "operations to evaluate our algorithm. In this setting, the user will first specify a set of handles used for", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 623, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 505, + 636 + ], + "score": 1.0, + "content": "manipulation (shown in Figure 5 in blue). In general, the user can apply three basic types of operation", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 635, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 635, + 506, + 646 + ], + "score": 1.0, + "content": "on a handle: 1) make it static (i.e., no deformation), 2) translate it, or 3) rotate it around a center.", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 645, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 645, + 506, + 658 + ], + "score": 1.0, + "content": "Usually, the first operation is used in combination with the latter two to produce useful deformation.", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "score": 1.0, + "content": "We first show how our algorithm deforms simple objects (e.g., a cylinder and a rectangle bar) when", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "the user rotates or translates one end while fixing the other. We then extend this set of operations to", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 678, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 506, + 691 + ], + "score": 1.0, + "content": "shapes with more detail (e.g., Cactus, Armadillo, and Dino). Finally, we test our algorithms when all", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 689, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 506, + 702 + ], + "score": 1.0, + "content": "three operations are specified together on a single shape. The results are shown in Figure 5. We can", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 700, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 106, + 700, + 506, + 713 + ], + "score": 1.0, + "content": "see that applying ARAP directly on the extracted mesh creates undesirable volume distortion. 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We apply the extension trick from Iglesias", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 272, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 106, + 272, + 505, + 284 + ], + "score": 1.0, + "content": "et al. [35] to create a matrix whose determinant equals the change of surface area. This is achieved by", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 282, + 506, + 296 + ], + "spans": [ + { + "bbox": [ + 106, + 282, + 256, + 296 + ], + "score": 1.0, + "content": "adding the surface normal component", + "type": "text" + }, + { + "bbox": [ + 257, + 282, + 284, + 295 + ], + "score": 0.92, + "content": "\\mathbf { n } _ { F } \\mathbf { n } _ { G } ^ { T }", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 282, + 506, + 296 + ], + "score": 1.0, + "content": "and keeping it unchanged. With this change of variable,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 294, + 504, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 397, + 305 + ], + "score": 1.0, + "content": "we now can compute the losses with point samples from the input field", + "type": "text" + }, + { + "bbox": [ + 397, + 294, + 406, + 304 + ], + "score": 0.82, + "content": "F", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 294, + 495, + 305 + ], + "score": 1.0, + "content": ". Since the input field", + "type": "text" + }, + { + "bbox": [ + 495, + 294, + 504, + 304 + ], + "score": 0.82, + "content": "F", + "type": "inline_equation" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 304, + 498, + 317 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 498, + 317 + ], + "score": 1.0, + "content": "approximates an SDF, we can use the method introduced in Section 5.1 to sample uniform points.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 258, + 506, + 317 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 328, + 187, + 340 + ], + "lines": [ + { + "bbox": [ + 105, + 326, + 189, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 189, + 343 + ], + "score": 1.0, + "content": "5.4 Optimization", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 108, + 348, + 504, + 360 + ], + "lines": [ + { + "bbox": [ + 105, + 347, + 505, + 362 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 505, + 362 + ], + "score": 1.0, + "content": "Putting the losses together, we deform a neural field by solving the constrained optimization problem", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22, + "bbox_fs": [ + 105, + 347, + 505, + 362 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 158, + 361, + 451, + 380 + ], + "lines": [ + { + "bbox": [ + 158, + 361, + 451, + 380 + ], + "spans": [ + { + "bbox": [ + 158, + 361, + 451, + 380 + ], + "score": 0.87, + "content": "\\underset { \\theta } { \\arg \\operatorname* { m i n } } \\lambda _ { s } \\mathcal { L } _ { s } ( G _ { \\theta } ) + \\lambda _ { b } \\mathcal { L } _ { b } ( G _ { \\theta } ) , \\quad \\mathrm { s . t . } \\forall 1 \\leq i \\leq n , \\ \\| D _ { \\theta } ( \\mathbf { t } _ { i } ) - \\mathbf { h } _ { i } \\| = 0", + "type": "interline_equation", + "image_path": "bc7131e80976def89d777867f865510168603474709b0e2f96c867263c85bc6b.jpg" + } + ] + } + ], + "index": 23, + "virtual_lines": [ + { + "bbox": [ + 158, + 361, + 451, + 380 + ], + "spans": [], + "index": 23 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 381, + 505, + 415 + ], + "lines": [ + { + "bbox": [ + 105, + 381, + 506, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 134, + 394 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 382, + 161, + 393 + ], + "score": 0.47, + "content": "\\lambda _ { s } , \\lambda _ { b }", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 381, + 506, + 394 + ], + "score": 1.0, + "content": "are hyperparameters that determine the material properties. One way to solve this", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 393, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 505, + 405 + ], + "score": 1.0, + "content": "constrained optimization problem for a neural network is to make the constraints a soft loss adding to", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 103, + 399, + 452, + 420 + ], + "spans": [ + { + "bbox": [ + 103, + 399, + 199, + 420 + ], + "score": 1.0, + "content": "the objective function:", + "type": "text" + }, + { + "bbox": [ + 199, + 402, + 356, + 416 + ], + "score": 0.88, + "content": "\\begin{array} { r } { \\dot { \\mathcal { L } } _ { c o n s t } ^ { { \\bf \\Delta } } ( D _ { \\theta } ) = \\frac { 1 } { n } \\sum _ { 1 = 1 } ^ { n } \\left. D _ { \\theta } ( \\mathbf { t } _ { i } ) - \\mathbf { h } _ { i } \\right. } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 399, + 452, + 420 + ], + "score": 1.0, + "content": ". Our final objective is:", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25, + "bbox_fs": [ + 103, + 381, + 506, + 420 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 218, + 417, + 392, + 430 + ], + "lines": [], + "index": 27, + "virtual_lines": [ + { + "bbox": [ + 218, + 417, + 392, + 430 + ], + "spans": [], + "index": 27 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 432, + 505, + 465 + ], + "lines": [ + { + "bbox": [ + 106, + 431, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 431, + 137, + 443 + ], + "score": 1.0, + "content": "We set", + "type": "text" + }, + { + "bbox": [ + 137, + 432, + 149, + 442 + ], + "score": 0.88, + "content": "\\lambda _ { c }", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 431, + 505, + 443 + ], + "score": 1.0, + "content": "to be a high value to enforce that the model satisfies user-specified input as much as", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 442, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 216, + 455 + ], + "score": 1.0, + "content": "possible. The user can tune", + "type": "text" + }, + { + "bbox": [ + 216, + 443, + 227, + 453 + ], + "score": 0.89, + "content": "\\lambda _ { b }", + "type": "inline_equation" + }, + { + "bbox": [ + 227, + 442, + 244, + 455 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 245, + 443, + 256, + 453 + ], + "score": 0.89, + "content": "\\lambda _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 442, + 463, + 455 + ], + "score": 1.0, + "content": "depending on the application scenario. We optimize", + "type": "text" + }, + { + "bbox": [ + 463, + 442, + 484, + 454 + ], + "score": 0.91, + "content": "\\mathcal { L } ( \\boldsymbol { \\theta } )", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 442, + 505, + 455 + ], + "score": 1.0, + "content": "with", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 453, + 491, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 453, + 274, + 465 + ], + "score": 1.0, + "content": "Adam optimizer to obtain the output field", + "type": "text" + }, + { + "bbox": [ + 274, + 453, + 288, + 464 + ], + "score": 0.89, + "content": "G _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 288, + 453, + 491, + 465 + ], + "score": 1.0, + "content": ". Hyperparameters are provided in the supplement.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 431, + 505, + 465 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 479, + 231, + 492 + ], + "lines": [ + { + "bbox": [ + 105, + 478, + 232, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 232, + 494 + ], + "score": 1.0, + "content": "6 Deformation Results", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 106, + 502, + 505, + 591 + ], + "lines": [ + { + "bbox": [ + 105, + 502, + 505, + 515 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 505, + 515 + ], + "score": 1.0, + "content": "In this section, we will demonstrate the results of our methods to shape deformation. The shapes", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 514, + 506, + 526 + ], + "spans": [ + { + "bbox": [ + 106, + 514, + 506, + 526 + ], + "score": 1.0, + "content": "for deformation are taken from Sorkine-Hornung and Alexa [70]. To create neural fields from these", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 525, + 505, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 505, + 537 + ], + "score": 1.0, + "content": "meshes, we follow the procedure of Park et al. [56] to compute ground-truth SDF for locations", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 535, + 506, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 172, + 548 + ], + "score": 1.0, + "content": "sampled within", + "type": "text" + }, + { + "bbox": [ + 172, + 535, + 204, + 547 + ], + "score": 0.92, + "content": "[ - 1 , 1 ] ^ { 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 535, + 506, + 548 + ], + "score": 1.0, + "content": ". We then fit a SIREN [66] to the ground-truth SDF to generate our initial", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 546, + 506, + 559 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 506, + 559 + ], + "score": 1.0, + "content": "neural fields. Our main baseline is ARAP [70, 86]. The simplest way to use ARAP to edit neural", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 556, + 506, + 570 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 506, + 570 + ], + "score": 1.0, + "content": "fields is applying it on a mesh extracted from the input neural fields using marching cubes [44, 45].", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 567, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 567, + 506, + 581 + ], + "score": 1.0, + "content": "We first present results comparing with ARAP applied to the extracted mesh. Then we will conduct", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 580, + 351, + 591 + ], + "spans": [ + { + "bbox": [ + 106, + 580, + 351, + 591 + ], + "score": 1.0, + "content": "an analysis to show our losses encourage the right behaviors.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 35.5, + "bbox_fs": [ + 105, + 502, + 506, + 591 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 601, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 601, + 505, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 601, + 505, + 614 + ], + "score": 1.0, + "content": "Comparing to ARAP baseline. We follow ARAP [70] to create a set of basic shape deformation", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 613, + 505, + 625 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 505, + 625 + ], + "score": 1.0, + "content": "operations to evaluate our algorithm. In this setting, the user will first specify a set of handles used for", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 623, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 505, + 636 + ], + "score": 1.0, + "content": "manipulation (shown in Figure 5 in blue). In general, the user can apply three basic types of operation", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 635, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 635, + 506, + 646 + ], + "score": 1.0, + "content": "on a handle: 1) make it static (i.e., no deformation), 2) translate it, or 3) rotate it around a center.", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 645, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 645, + 506, + 658 + ], + "score": 1.0, + "content": "Usually, the first operation is used in combination with the latter two to produce useful deformation.", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "score": 1.0, + "content": "We first show how our algorithm deforms simple objects (e.g., a cylinder and a rectangle bar) when", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "the user rotates or translates one end while fixing the other. We then extend this set of operations to", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 678, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 506, + 691 + ], + "score": 1.0, + "content": "shapes with more detail (e.g., Cactus, Armadillo, and Dino). Finally, we test our algorithms when all", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 689, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 506, + 702 + ], + "score": 1.0, + "content": "three operations are specified together on a single shape. The results are shown in Figure 5. We can", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 700, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 106, + 700, + 506, + 713 + ], + "score": 1.0, + "content": "see that applying ARAP directly on the extracted mesh creates undesirable volume distortion. Our", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 711, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 711, + 506, + 723 + ], + "score": 1.0, + "content": "algorithm is able to produce deformation results that are natural while satisfying the user’s intention.", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 45, + "bbox_fs": [ + 105, + 601, + 506, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 106, + 73, + 504, + 435 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 106, + 73, + 504, + 435 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 73, + 504, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 504, + 435 + ], + "score": 0.976, + "type": "image", + "image_path": "4b0800ba8a5e03bd4ddc57775de98cce018d0745cceb87a6a5d10c6b16f46363.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 106, + 73, + 504, + 193.66666666666669 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 106, + 193.66666666666669, + 504, + 314.33333333333337 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 106, + 314.33333333333337, + 504, + 435.00000000000006 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 443, + 506, + 488 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 443, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 506, + 456 + ], + "score": 1.0, + "content": "Figure 5: Deformation results. (A) Input shape. (B) Baseline. (C) Ours. Red points are user specified", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 454, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 454, + 138, + 468 + ], + "score": 1.0, + "content": "handles", + "type": "text" + }, + { + "bbox": [ + 138, + 455, + 150, + 466 + ], + "score": 0.86, + "content": "\\mathbf { h } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 150, + 454, + 336, + 468 + ], + "score": 1.0, + "content": ". Blue points denote user specified target points", + "type": "text" + }, + { + "bbox": [ + 337, + 456, + 346, + 466 + ], + "score": 0.86, + "content": "\\mathbf { t } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 454, + 506, + 468 + ], + "score": 1.0, + "content": ". First row: single rotation or translation", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 466, + 507, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 507, + 479 + ], + "score": 1.0, + "content": "on simple shapes. Second and third rows: single rotation or translation on more complex objects.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 476, + 295, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 476, + 295, + 489 + ], + "score": 1.0, + "content": "Fourth row: multiple edits on complex objects.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 107, + 500, + 505, + 621 + ], + "lines": [ + { + "bbox": [ + 106, + 500, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 500, + 505, + 513 + ], + "score": 1.0, + "content": "Comparing to different ARAP variants. This artifact is partially due to the surface discretization", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 511, + 506, + 523 + ], + "spans": [ + { + "bbox": [ + 106, + 511, + 506, + 523 + ], + "score": 1.0, + "content": "made by the marching cubed algorithm doesn’t agree with the assumptions made by ARAP [41].", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 522, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 505, + 534 + ], + "score": 1.0, + "content": "To verify this hypothesis, we also include three additional baselines in Figure 6. First, we show the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 533, + 506, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 506, + 546 + ], + "score": 1.0, + "content": "results of applying ARAP on the low-poly mesh used to create the input neural fields (Original).", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 544, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 544, + 505, + 556 + ], + "score": 1.0, + "content": "Second, we first apply Garland and Heckbert [28] to simplify the surface of the extracted mesh before", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 555, + 506, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 506, + 567 + ], + "score": 1.0, + "content": "applying ARAP to it (Remeshed). Finally, we also compare to the results of SR-ARAP [41], which", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "score": 1.0, + "content": "adds smoothness regularization to ARAP to remove some unnatural distortion (SR-ARAP). The figure", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 576, + 505, + 589 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 505, + 589 + ], + "score": 1.0, + "content": "shows that ARAP works much better when the surface is discretized appropriately. Discretizing the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 587, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 106, + 587, + 505, + 600 + ], + "score": 1.0, + "content": "surface, however, usually requires case-by-case manual adjustment to perform well. Our algorithm", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 598, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 598, + 505, + 612 + ], + "score": 1.0, + "content": "does not suffer from such issues as we optimize the thin shell objective directly without committing", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 610, + 280, + 622 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 280, + 622 + ], + "score": 1.0, + "content": "to a particular discretization of the surface.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 634, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 634, + 505, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 505, + 647 + ], + "score": 1.0, + "content": "Loss analysis. Here we provide an experiment to analyze the behavior of stretching loss and", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 645, + 505, + 658 + ], + "spans": [ + { + "bbox": [ + 106, + 645, + 453, + 658 + ], + "score": 1.0, + "content": "bending loss. Specifically, we compare models optimized for only the stretching loss", + "type": "text" + }, + { + "bbox": [ + 453, + 646, + 465, + 656 + ], + "score": 0.88, + "content": "\\mathcal { L } _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 466, + 645, + 505, + 658 + ], + "score": 1.0, + "content": ", only the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 161, + 668 + ], + "score": 1.0, + "content": "bending loss", + "type": "text" + }, + { + "bbox": [ + 162, + 657, + 173, + 667 + ], + "score": 0.88, + "content": "\\mathcal { L } _ { b }", + "type": "inline_equation" + }, + { + "bbox": [ + 174, + 656, + 505, + 668 + ], + "score": 1.0, + "content": ", and both losses together. Similar to Section 5.2, we deform a neural field that", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 667, + 504, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 491, + 680 + ], + "score": 1.0, + "content": "approximates the SDF of a 2D rectangle. The results are shown in Figure 7. Optimizing only for", + "type": "text" + }, + { + "bbox": [ + 492, + 667, + 504, + 678 + ], + "score": 0.88, + "content": "\\mathcal { L } _ { s }", + "type": "inline_equation" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 678, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 505, + 691 + ], + "score": 1.0, + "content": "produces a shape that best preserves surface area (or the perimeter in the 2D case), which explains", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 689, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 245, + 701 + ], + "score": 1.0, + "content": "the wiggling. Optimizing only for", + "type": "text" + }, + { + "bbox": [ + 245, + 689, + 257, + 700 + ], + "score": 0.89, + "content": "\\mathcal { L } _ { b }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 689, + 506, + 701 + ], + "score": 1.0, + "content": "produces a shape that tries to prevent wiggling of the surface,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 417, + 712 + ], + "score": 1.0, + "content": "which changes the curvature of the surface. The user can choose appropriate", + "type": "text" + }, + { + "bbox": [ + 417, + 700, + 429, + 711 + ], + "score": 0.88, + "content": "\\lambda _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 429, + 699, + 447, + 712 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 447, + 700, + 458, + 711 + ], + "score": 0.88, + "content": "\\lambda _ { b }", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "to produce", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 710, + 345, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 345, + 723 + ], + "score": 1.0, + "content": "deformation with resistance to both bending and stretching.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 21.5 + } + ], + "page_idx": 8, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 742, + 308, + 750 + ], + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 752 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 752 + ], + "score": 1.0, + "content": "9", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 106, + 73, + 504, + 435 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 106, + 73, + 504, + 435 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 73, + 504, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 504, + 435 + ], + "score": 0.976, + "type": "image", + "image_path": "4b0800ba8a5e03bd4ddc57775de98cce018d0745cceb87a6a5d10c6b16f46363.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 106, + 73, + 504, + 193.66666666666669 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 106, + 193.66666666666669, + 504, + 314.33333333333337 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 106, + 314.33333333333337, + 504, + 435.00000000000006 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 443, + 506, + 488 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 443, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 506, + 456 + ], + "score": 1.0, + "content": "Figure 5: Deformation results. (A) Input shape. (B) Baseline. (C) Ours. Red points are user specified", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 454, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 454, + 138, + 468 + ], + "score": 1.0, + "content": "handles", + "type": "text" + }, + { + "bbox": [ + 138, + 455, + 150, + 466 + ], + "score": 0.86, + "content": "\\mathbf { h } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 150, + 454, + 336, + 468 + ], + "score": 1.0, + "content": ". Blue points denote user specified target points", + "type": "text" + }, + { + "bbox": [ + 337, + 456, + 346, + 466 + ], + "score": 0.86, + "content": "\\mathbf { t } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 454, + 506, + 468 + ], + "score": 1.0, + "content": ". First row: single rotation or translation", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 466, + 507, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 507, + 479 + ], + "score": 1.0, + "content": "on simple shapes. Second and third rows: single rotation or translation on more complex objects.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 476, + 295, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 476, + 295, + 489 + ], + "score": 1.0, + "content": "Fourth row: multiple edits on complex objects.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 107, + 500, + 505, + 621 + ], + "lines": [ + { + "bbox": [ + 106, + 500, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 500, + 505, + 513 + ], + "score": 1.0, + "content": "Comparing to different ARAP variants. This artifact is partially due to the surface discretization", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 511, + 506, + 523 + ], + "spans": [ + { + "bbox": [ + 106, + 511, + 506, + 523 + ], + "score": 1.0, + "content": "made by the marching cubed algorithm doesn’t agree with the assumptions made by ARAP [41].", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 522, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 505, + 534 + ], + "score": 1.0, + "content": "To verify this hypothesis, we also include three additional baselines in Figure 6. First, we show the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 533, + 506, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 506, + 546 + ], + "score": 1.0, + "content": "results of applying ARAP on the low-poly mesh used to create the input neural fields (Original).", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 544, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 544, + 505, + 556 + ], + "score": 1.0, + "content": "Second, we first apply Garland and Heckbert [28] to simplify the surface of the extracted mesh before", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 555, + 506, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 506, + 567 + ], + "score": 1.0, + "content": "applying ARAP to it (Remeshed). Finally, we also compare to the results of SR-ARAP [41], which", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "score": 1.0, + "content": "adds smoothness regularization to ARAP to remove some unnatural distortion (SR-ARAP). The figure", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 576, + 505, + 589 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 505, + 589 + ], + "score": 1.0, + "content": "shows that ARAP works much better when the surface is discretized appropriately. Discretizing the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 587, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 106, + 587, + 505, + 600 + ], + "score": 1.0, + "content": "surface, however, usually requires case-by-case manual adjustment to perform well. Our algorithm", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 598, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 598, + 505, + 612 + ], + "score": 1.0, + "content": "does not suffer from such issues as we optimize the thin shell objective directly without committing", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 610, + 280, + 622 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 280, + 622 + ], + "score": 1.0, + "content": "to a particular discretization of the surface.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 500, + 506, + 622 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 634, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 634, + 505, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 505, + 647 + ], + "score": 1.0, + "content": "Loss analysis. Here we provide an experiment to analyze the behavior of stretching loss and", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 645, + 505, + 658 + ], + "spans": [ + { + "bbox": [ + 106, + 645, + 453, + 658 + ], + "score": 1.0, + "content": "bending loss. Specifically, we compare models optimized for only the stretching loss", + "type": "text" + }, + { + "bbox": [ + 453, + 646, + 465, + 656 + ], + "score": 0.88, + "content": "\\mathcal { L } _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 466, + 645, + 505, + 658 + ], + "score": 1.0, + "content": ", only the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 161, + 668 + ], + "score": 1.0, + "content": "bending loss", + "type": "text" + }, + { + "bbox": [ + 162, + 657, + 173, + 667 + ], + "score": 0.88, + "content": "\\mathcal { L } _ { b }", + "type": "inline_equation" + }, + { + "bbox": [ + 174, + 656, + 505, + 668 + ], + "score": 1.0, + "content": ", and both losses together. Similar to Section 5.2, we deform a neural field that", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 667, + 504, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 491, + 680 + ], + "score": 1.0, + "content": "approximates the SDF of a 2D rectangle. The results are shown in Figure 7. Optimizing only for", + "type": "text" + }, + { + "bbox": [ + 492, + 667, + 504, + 678 + ], + "score": 0.88, + "content": "\\mathcal { L } _ { s }", + "type": "inline_equation" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 678, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 505, + 691 + ], + "score": 1.0, + "content": "produces a shape that best preserves surface area (or the perimeter in the 2D case), which explains", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 689, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 245, + 701 + ], + "score": 1.0, + "content": "the wiggling. Optimizing only for", + "type": "text" + }, + { + "bbox": [ + 245, + 689, + 257, + 700 + ], + "score": 0.89, + "content": "\\mathcal { L } _ { b }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 689, + 506, + 701 + ], + "score": 1.0, + "content": "produces a shape that tries to prevent wiggling of the surface,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 417, + 712 + ], + "score": 1.0, + "content": "which changes the curvature of the surface. 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Directly applying ARAP to extracted mesh produces", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 180, + 506, + 194 + ], + "spans": [ + { + "bbox": [ + 104, + 180, + 506, + 194 + ], + "score": 1.0, + "content": "poor results (i.e., MC). While this can be alleviated by remshing (i.e. Original or Remeshed)", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 191, + 506, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 506, + 205 + ], + "score": 1.0, + "content": "or regularization (i.e. SR-ARAP), this shows mesh deformation algorithms can be sensitive to", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 202, + 506, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 506, + 215 + ], + "score": 1.0, + "content": "discretization quality. Our method do not discretize the surface, thus circumvent such issue. Red", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 214, + 278, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 278, + 227 + ], + "score": 1.0, + "content": "points are handles; Blue points are targets.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "title", + "bbox": [ + 107, + 244, + 337, + 258 + ], + "lines": [ + { + "bbox": [ + 104, + 243, + 340, + 261 + ], + "spans": [ + { + "bbox": [ + 104, + 243, + 340, + 261 + ], + "score": 1.0, + "content": "7 Discussion, Limitations, and Future work", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 269, + 337, + 389 + ], + "lines": [ + { + "bbox": [ + 105, + 268, + 338, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 338, + 282 + ], + "score": 1.0, + "content": "Advantages of using neural fields for geometry pro-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 280, + 338, + 292 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 338, + 292 + ], + "score": 1.0, + "content": "cessing. The main strength of using neural fields for", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 291, + 338, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 338, + 304 + ], + "score": 1.0, + "content": "geometry processing is that one can disentangle the pro-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 302, + 337, + 313 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 337, + 313 + ], + "score": 1.0, + "content": "cessing algorithm from the surface discretization. Users", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 313, + 338, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 313, + 338, + 325 + ], + "score": 1.0, + "content": "do not need to worry about discretization while manipulat-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 323, + 337, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 337, + 336 + ], + "score": 1.0, + "content": "ing a shape represented in neural fields. This might open", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 334, + 339, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 339, + 347 + ], + "score": 1.0, + "content": "the door to more automatic geometry processing pipelines.", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 345, + 338, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 345, + 338, + 357 + ], + "score": 1.0, + "content": "Additionally, neural fields are modular and can be com-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 356, + 337, + 368 + ], + "spans": [ + { + "bbox": [ + 106, + 356, + 337, + 368 + ], + "score": 1.0, + "content": "bined with other neural networks. 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Potential negative impact includes", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 562, + 388, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 562, + 388, + 574 + ], + "score": 1.0, + "content": "misuse of geometry processing algorithms to create offensive content.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 38, + "bbox_fs": [ + 105, + 539, + 505, + 574 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 588, + 183, + 602 + ], + "lines": [ + { + "bbox": [ + 104, + 586, + 185, + 604 + ], + "spans": [ + { + "bbox": [ + 104, + 586, + 185, + 604 + ], + "score": 1.0, + "content": "8 Conclusion", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 107, + 613, + 505, + 668 + ], + "lines": [ + { + "bbox": [ + 105, + 613, + 505, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 505, + 626 + ], + "score": 1.0, + "content": "Our work provides a proof of concept that geometry processing can be done entirely with neural", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 624, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 505, + 636 + ], + "score": 1.0, + "content": "fields without discretizing the surface. We develop network architectures and training objectives", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 635, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 506, + 648 + ], + "score": 1.0, + "content": "for filtering and deforming shapes represented by neural fields and demonstrate the advantages of", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 645, + 506, + 659 + ], + "spans": [ + { + "bbox": [ + 105, + 645, + 506, + 659 + ], + "score": 1.0, + "content": "using neural fields for geometry processing. We hope that our work can inspire a new generation of", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 658, + 315, + 670 + ], + "spans": [ + { + "bbox": [ + 105, + 658, + 315, + 670 + ], + "score": 1.0, + "content": "geometry processing algorithms using neural fields.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 43, + "bbox_fs": [ + 105, + 613, + 506, + 670 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 675, + 503, + 708 + ], + "lines": [ + { + "bbox": [ + 106, + 675, + 505, + 687 + ], + "spans": [ + { + "bbox": [ + 106, + 675, + 505, + 687 + ], + "score": 1.0, + "content": "Acknowledgement. Guandao’s PhD was supported in part by a research gift from Magic Leap and", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 686, + 505, + 698 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 505, + 698 + ], + "score": 1.0, + "content": "a donation from NVIDIA. 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Dino Armadillo
MetricsLDOursLDOurs
CDr (↓)1.541.041.361.02
EMDr (↓)3.381.153.301.08
Time0.150.210.120.18
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index 0000000000000000000000000000000000000000..d6304df1207a359bf69132f1d2fcc0b3b3b25f30 --- /dev/null +++ b/parse/train/rJeU_1SFvr/rJeU_1SFvr.md @@ -0,0 +1,518 @@ +# LOGAN: LATENT OPTIMISATION FOR GENERATIVEADVERSARIAL NETWORKS + +Anonymous authors Paper under double-blind review + +# ABSTRACT + +Training generative adversarial networks requires balancing of delicate adversarial dynamics. Even with careful tuning, training may diverge or end up in a bad equilibrium with dropped modes. In this work, we introduce a new form of latent optimisation inspired by the CS-GAN and show that it improves adversarial dynamics by enhancing interactions between the discriminator and the generator. We develop supporting theoretical analysis from the perspectives of differentiable games and stochastic approximation. Our experiments demonstrate that latent optimisation can significantly improve GAN training, obtaining state-of-the-art performance for the ImageNet $1 2 8 \times 1 2 8 )$ dataset. Our model achieves an Inception Score (IS) of 148 and an Frechet Inception Distance (FID) of ´ 3.4, an improvement of $1 7 \%$ and $3 2 \%$ in IS and FID respectively, compared with the baseline BigGAN-deep model with the same architecture and number of parameters. + +# 1 INTRODUCTION + +Generative Adversarial Nets (GANs) are implicit generative models that can be trained to match a given data distribution. GANs were originally proposed and demonstrated for images by Goodfellow et al. (2014). As the field of generative modelling has advanced, GANs have remained at the frontier, generating high-fidelity images at large scale (Brock et al., 2018). However, despite growing insights into the dynamics of GAN training, most recent advances in large-scale image generation come from architectural improvements (Radford et al., 2015; Zhang et al., 2019), or regularisation focusing on particular parts of the model (Miyato et al., 2018; Miyato & Koyama, 2018). Inspired by the compressed sensing GAN (CS-GAN; Wu et al., 2019), we further exploit the benefit of latent optimisation in adversarial games using natural gradient descent to optimise the latent variable $z$ at each step of training, presenting a scalable and easy to implement approach to improve the dynamical interaction between the discriminator and the generator. For clarity, we unify these approaches as latent optimised GANs (LOGAN). + +To summarise our contributions: + +1. We present a novel analysis of latent optimisation in GANs from the perspective of differentiable games and stochastic approximation (Balduzzi et al., 2018; Heusel et al., 2017), arguing that latent optimisation can improve the dynamics of adversarial training. 2. Motivated by this analysis, we improve latent optimisation by taking advantage of efficient second-order updates. 3. Our algorithm improves the state-of-the-art BigGAN-deep model (Brock et al., 2018) by a significant margin, without introducing any architectural change or additional parameters, resulting in higher quality images and more diverse samples (Figure 1 and 2). + +# 2 BACKGROUND + +# 2.1 NOTATION + +We use $\theta _ { D }$ and $\theta _ { G }$ to denote the vectors representing parameters of the generator and discriminator. We use $x$ for images, and $z$ for the latent source generating an image. The prime 0 is used to denote + +![](images/940acc1b2137ed3db28ecc22572b29ae004f7f4763b437aab5109fd2ff070819.jpg) +Figure 1: Samples from BigGAN-deep (a) and LOGAN (b) with similarly high IS. Samples from the two panels were drawn from truncation levels corresponding to points C and D in figure $^ { 3 \mathrm { ~ b ~ } }$ respectively. (FID/IS: (a) 27.97/259.4, (b) 8.19/259.9) + +![](images/86601a8a9e19d78392a2f54a737be755f53742c748082b3e5d2bcc4246e83a01.jpg) +Figure 2: Samples from BigGAN-deep (a) and LOGAN (b) with similarly low FID. Samples from the two panels were drawn from truncation levels corresponding to points A and $\mathbf { B }$ in figure $^ { 3 \mathrm { ~ b ~ } }$ respectively. (FID/IS: (a) 5.04/126.8, (b) 5.09/217.0) + +a variable after one update step, e.g., $\begin{array} { r } { \theta _ { D } ^ { \prime } = \theta _ { D } - \alpha \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { D } } } \end{array}$ . $p ( x )$ and $p ( z )$ denote the data distribution and source distribution respectively. $\mathbb { E } _ { p ( x ) } \left[ f ( x ) \right]$ indicates taking the expectation of function $f ( x )$ over the distribution $p ( x )$ . + +# 2.2 GENERATIVE ADVERSARIAL NETS + +A GAN consists of a generator that generates image $x = G ( z ; \theta _ { G } )$ from a latent source $z \sim p ( z )$ , and a discriminator that scores the generated images as $D ( x ; \theta _ { D } )$ (Goodfellow et al., 2014). Training GANs involves an adversarial game: while the discriminator tries to distinguish generated samples $x = G \left( z ; \theta _ { G } \right)$ from data $x \sim p ( x )$ , the generator tries to fool the discriminator. This procedure can be summarised as the following min-max game: + +$$ +\operatorname* { m i n } _ { \theta _ { D } } \operatorname* { m a x } _ { \theta _ { G } } \mathbb { E } _ { z \sim p ( x ) } [ h _ { D } ( D ( x ; \theta _ { D } ) ) ] + \mathbb { E } _ { z \sim p ( z ) } [ h _ { G } ( D ( G ( z ; \theta _ { G } ) ; \theta _ { D } ) ) ] +$$ + +Table 1: Comparison of model scores. BigGAN-deep results are reproduced from Brock et al. (2018). “baseline” indicates our reproduced BigGAN-deep with small modifications. The 3rd and 4th columns are from the gradient descent (GD, ablated) and natural gradient descent (NGD) versions of LOGAN respectively. We report the Inception Score (IS, higher is better, Salimans et al. 2016) and Frechet Inception Distance (FID, lower is better, Heusel et al. 2017). ´ + +
BigGAN-DeepbaselineLOGAN (GD)LOGAN (NGD)
FID5.7 ± 0.34.92±0.054.86±0.093.36± 0.14
IS124.5 ± 2.0126.6 ± 1.3127.7 ± 3.5148.2 ±3.1
+ +The exact form of $h ( \cdot )$ depends on the choice of loss function (Goodfellow et al., 2014; Arjovsky et al., 2017; Nowozin et al., 2016). To simplify our presentation and analysis, we use the Wasserstein loss (Arjovsky et al., 2017), so that $h _ { D } ( t ) = - t$ and $h _ { G } ( t ) = t$ . Our experiments with BigGANdeep uses the hinge loss (Lim & Ye, 2017; Tran et al., 2017), which is identical to this form in its linear regime. Our analysis can be generalised to other losses as in previous theoretical work (e.g., Arora et al. 2017). To simplify notation, we abbreviate $f ( z ; \theta _ { D } , \bar { \theta _ { G } } ) = D \left( G \left( z ; \theta _ { G } \right) ; \theta _ { D } \right)$ , which may be further simplified as $f ( z )$ when the explicit dependency on $\theta _ { D }$ and $\theta _ { G }$ can be omitted. + +Training GANs requires carefully balancing updates to $D$ and $G$ , and is sensitive to both architecture and algorithm choices (Salimans et al., 2016; Radford et al., 2015). A recent milestone is BigGAN (and BigGAN-deep, Brock et al. 2018), which pushed the boundary of high fidelity image generation by scaling up GANs to an unprecedented level. BigGANs use an architecture based on residual blocks (He et al., 2016), in combination with regularisation mechanisms and self-attention (Saxe et al., 2014; Miyato et al., 2018; Zhang et al., 2019). + +Here we aim to improve the adversarial dynamics during training. We focus on the second term in eq. 1 which is at the heart of the min-max game, with adversarial losses for $D$ and $G$ , which can be written as + +$$ +L ( z ) = \left[ L _ { D } ( z ) , L _ { G } ( z ) \right] ^ { T } = \left[ f ( z ) , - f ( z ) \right] ^ { T } +$$ + +Computing the gradients with respect to $\theta _ { D }$ and $\theta _ { G }$ obtains the following gradient, which cannot be expressed as the gradient of any single function (Balduzzi et al., 2018): + +$$ +g = \left[ \frac { \partial L _ { D } ( z ) } { \partial \theta _ { D } } , \frac { \partial L _ { G } ( z ) } { \partial \theta _ { G } } \right] ^ { T } = \left[ \frac { \partial f ( z ) } { \partial \theta _ { D } } , - \frac { \partial f ( z ) } { \partial \theta _ { G } } \right] ^ { T } +$$ + +The fact that $g$ is not the gradient of a function implies that gradient updates in GANs can exhibit cycling behaviour which can slow down or prevent convergence. In Balduzzi et al. (2018), vector fields of this form are referred to as the simultaneous gradient. Although many GAN models use alternating update rules (e.g., Goodfellow et al. 2014; Brock et al. 2018), following the gradient with respect to $\theta _ { D }$ and $\theta _ { G }$ alternatively in each step, they can still suffer from cycling, so we use the simpler simultaneous gradient (eq. 3) for our analysis. + +# 2.3 LATENT OPTIMISED GANS + +Inspired by compressed sensing (Candes et al., 2006; Donoho, 2006), Wu et al. (2019) introduced latent optimisation for GANs. We call this type of model latent-optimised GANs (LOGAN). Latent optimization has been shown to improve the stability of training as well as the final performance for medium-sized models such as DCGANs and Spectral Normalised GANs (Radford et al., 2015; Miyato et al., 2018). Latent optimisation exploits knowledge from $D$ to guide updates of $z$ . Intuitively, the gradient $\begin{array} { r } { \nabla _ { z } f ( z ) = \frac { \partial f ( z ) } { \partial z } } \end{array}$ points in the direction that satisfies the discriminator $D$ , which implies better samples. Therefore, instead of using the randomly sampled $z \sim p ( z )$ , Wu et al. (2019) uses the optimised latent + +$$ +\Delta z = \alpha \frac { \partial f ( z ) } { \partial z } \qquad z ^ { \prime } = z + \Delta z +$$ + +in eq. 1 for training 1. The general algorithm is summarised in Algorithm 1 and illustrated in Figure 3 a. We develop the natural gradient descent form of latent update in Section 4. + +![](images/c24ba41202d98dd0cfb864fbd092fb035f3fe4c84763666ad586e37a8cf9c30d.jpg) +Figure 3: (a) Schematic of LOGAN. We first compute a forward pass through $G$ and $D$ with a sampled latent $z$ . Then, gradients from the generator loss (dashed red arrow) are used to compute an improved latent, $z ^ { \prime }$ . After this optimised latent code is used in a second forward pass, we compute gradients of the discriminator back through the latent optimisation into the model parameters $\theta _ { D }$ , $\theta _ { G }$ . These gradients are used to update the model. (b) Truncation curves illustrate the FID/IS tradeoff for each model by altering the range of the noise source $p ( z )$ . GD: gradient descent. NGD: natural gradient descent. Points A, B, C, D correspond to samples shown in Figure 1 and 2. + +Algorithm 1 Latent Optimised GANs with Automatic Differentiation + +
Input: data distribution p(x),latent distribution p(z),D(:; 0D), G(-; 0g),learning rate α, batch size N repeat
Initialise discriminator and generator parameters 0D,0G fori=1 to Ndo
Sample z ~ p(z),x~p(x)
Compute the gradient D(G(z)) and use it to obtain △z from eq. 4 (GD) or eq. 12 (NGD) dz
Optimise the latent z' ← [+ △z],[:] indicates clipping the value between -1 and 1
= -D(G(z))
D(G(z'))-D(x) end for
Compute batch losses LG =N∑i=11 JN (i) and LD=∑=1 N L(i) LD
aLD aLG Update 0D and 0G with the gradients
0D， G
until reaches the maximum training steps
+ +# 3 ANALYSIS OF THE ALGORITHM + +To understand how latent optimisation improves GAN training, we analyse LOGAN as a 2-player differentiable game following Balduzzi et al. (2018); Gemp & Mahadevan (2018); Letcher et al. (2019). The appendix provides a complementary analysis that relates LOGAN to unrolled GANs (Metz et al., 2016) and stochastic approximation (Heusel et al., 2017; Borkar, 1997). + +# 3.1 THE SYMPLECTIC GRADIENT ADJUSTMENT (SGA) + +An important problem with gradient-based optimization in GANs is that the vector-field generated by the losses of the discriminator and generator is not a gradient vector field. It follows that gradient descent is not guaranteed to find a local optimum and can cycle, which can slow down convergence or lead to phenomena like mode collapse and mode hopping. Balduzzi et al. (2018); Gemp & + +Mahadevan (2018) proposed Symplectic Gradient Adjustment (SGA) to improve the dynamics of gradient-based methods in adversarial games. For a game with gradient $g$ (eq. 3), define the Hessian as the second order derivatives with respect to the parameters, $H = \nabla _ { \theta } g$ . SGA uses the adjusted gradient + +$$ +g ^ { * } = g + \lambda A ^ { T } g \quad { \mathrm { w h e r e ~ } } \lambda { \mathrm { ~ i s ~ a ~ p o s i t i v e ~ c o n s t a n t } } +$$ + +and $\begin{array} { r } { A = \frac 1 2 ( H - H ^ { T } ) } \end{array}$ is the anti-symmetric component of the Hessian. Applying SGA to GANs yields the adjusted updates (see Appendix B.1 for details): + +$$ +g ^ { \ast } = \left[ \frac { \partial f ( z ) } { \partial \theta _ { D } } + \lambda \left( \frac { \partial ^ { 2 } f ( z ) } { \partial \theta _ { G } \partial \theta _ { D } } \right) ^ { T } \frac { \partial f ( z ) } { \partial \theta _ { G } } , - \frac { \partial f ( z ) } { \partial \theta _ { G } } + \lambda \left( \frac { \partial ^ { 2 } f ( z ) } { \partial \theta _ { D } \partial \theta _ { G } } \right) ^ { T } \frac { \partial f ( z ) } { \partial \theta _ { D } } \right] ^ { T } +$$ + +Compared with $g$ in eq. 3, the adjusted gradient $g ^ { * }$ has second-order terms reflecting the interactions between $D$ and $G$ . SGA has been shown to significantly improve GAN training in basic examples (Balduzzi et al., 2018), allowing faster and more robust convergence to stable fixed points (local Nash equilibria). Unfortunately, SGA is expensive to scale because computing the second-order derivatives with respect to all parameters is expensive. + +Explicitly computing the gradients for the discriminator and generator at $z ^ { \prime }$ after one step of latent optimisation (eq. 4) obtains + +$$ +\begin{array} { r l r } & { } & { \left[ \frac { d L _ { D } } { d \theta _ { D } } , \frac { d L _ { G } } { d \theta _ { G } } \right] } ^ { T } = { { \left[ \frac { \partial f ( { \boldsymbol { z } } ^ { \prime } ) } { \partial \theta _ { D } } + \left( \frac { \partial \Delta { \boldsymbol { z } } } { \partial \theta _ { D } } \right) ^ { T } \frac { \partial f ( { \boldsymbol { z } } ^ { \prime } ) } { \partial \Delta { \boldsymbol { z } } } , - \frac { \partial f ( { \boldsymbol { z } } ^ { \prime } ) } { \partial \theta _ { G } } - \left( \frac { \partial \Delta { \boldsymbol { z } } } { \partial \theta _ { G } } \right) ^ { T } \frac { \partial f ( { \boldsymbol { z } } ^ { \prime } ) } { \partial \Delta { \boldsymbol { z } } } \right] } ^ { T } { \left( \boldsymbol { \hat { z } } ^ { \prime } \right) } } \\ & { } & { = { { \left[ \frac { \partial f ( { \boldsymbol { z } } ^ { \prime } ) } { \partial \theta _ { D } } + \alpha \left( \frac { \partial ^ { 2 } f ( { \boldsymbol { z } } ) } { \partial \boldsymbol { z } \partial \theta _ { D } } \right) ^ { T } \frac { \partial f ( { \boldsymbol { z } } ^ { \prime } ) } { \partial { \boldsymbol { z } } ^ { \prime } } , - \frac { \partial f ( { \boldsymbol { z } } ^ { \prime } ) } { \partial \theta _ { G } } - \alpha \left( \frac { \partial ^ { 2 } f ( { \boldsymbol { z } } ) } { \partial \boldsymbol { z } \partial \theta _ { G } } \right) ^ { T } \frac { \partial f ( { \boldsymbol { z } } ^ { \prime } ) } { \partial { \boldsymbol { z } } ^ { \prime } } \right] } ^ { T } } } \end{array} +$$ + +In both equations, the first terms represent how $f ( z ^ { \prime } )$ depends on the parameters directly and the second terms represent how $f ( z ^ { \prime } )$ depends on the parameters via the optimised latent source. For the second equality, we substitute $\begin{array} { r } { \Delta z = \alpha \frac { \partial f ( z ) } { \partial z } } \end{array}$ as the gradient-based update of $z$ and use $\begin{array} { r } { \frac { \partial f ( z ^ { \prime } ) } { \partial \Delta z } = } \end{array}$ ∂f(z0)∂z0 . The original GAN’s gradient (eq. 3) does not include any second-order term, since ∆z = 0 without latent optimisation. In LOGAN, these extra terms are computed by automatic differentiation when back-propagating through the latent optimisation process (see Algorithm 1). + +The SGA updates in eq. 6 and the LOGAN updates in eq. 8 are strikingly similar, suggesting that the latent step used by LOGAN reduces the negative effects of cycling by introducing a symplectic gradient adjustment into the optimization procedure. The role of the latent step can be formalized in terms of a third player, whose goal is to help the generator, see appendix B for details. + +Crucially, latent optimisation approximates SGA using only second-order derivatives with respect to the latent $z$ and parameters of the discriminator and generator separately. The second order terms involving parameters of both the discriminator and the generator – which are extremely expensive to compute – are not used. For latent $z$ ’s with dimensions typically used in GANs (e.g., 128–256, orders of magnitude less than the number of parameters), these can be computed efficiently. In short, latent optimisation efficiently couples the gradients of the discriminator and generator, as prescribed by SGA, but using the much lower-dimensional latent source $z$ which makes the adjustment scalable. + +An important consequence of reducing the rotational aspect of GAN dynamics is that it is possible to use larger step sizes during training which suggests using stronger optimisers to fully take advantage of latent optimisation. Latent optimisation can improve GAN training dynamics further by allowing larger single steps $\Delta z$ towards the direction of $\frac { \partial f ( z ) } { \partial z }$ ) without overshooting. + +# 3.2 UNROLLING AND STOCHASTIC APPROXIMATION + +Appendix B further explains how LOGAN relates to unrolled GANs (Metz et al., 2016) and stochastic approximation. Our main finding is that latent optimisation accelerates the speed of updating $D$ relative to that of $G$ , facilitating convergence according to Heusel et al. (2017) (see also Figure ${ } 4 \mathbf { b }$ ). In particular, the generator requires less update compared with $D$ to achieve the same reduction of loss, because latent optimisation “helps” $G$ . + +![](images/a79b2b3f2b5f754129923560fbb71709f81bf8416d83d1a5b7fe6082daa4985c.jpg) +Figure 4: (a) Scaling of gradients in natural gradient descent. We use $\beta = 5$ in BigGAN-Deep experiments. (b) The update speed of the discriminator relative to the generator shown as the difference $\lVert \Delta \boldsymbol { \theta } _ { D } \rVert - \lVert \Delta \boldsymbol { \theta } _ { G } \rVert$ after each update step. Lines are smoothed with moving average using window size 20 (in total, there are 3007, 1659 and 1768 data points for each curve). For all curves oscillation strongly after training collapsed. + +# 4 LOGAN WITH NATURAL GRADIENT DESCENT + +Although our analysis suggests using strong optimisers for optimising $z$ , Wu et al. (2019) only used basic gradient descent (GD) with a fixed step-size. This choice limits the size $\Delta z$ can take: in order not to overshoot when the curvature is large, the step size would be too conservative when the curvature is small. We hypothesis that GD is more detrimental for larger models, which have complex loss surfaces with highly varying curvatures. Consistent with this hypothesis, we observed only marginal improvement over the baseline using GD (section 5.3, Table 1, Figure $3 \mathbf { b }$ ). + +In this work, we instead use natural gradient descent (NGD, Amari 1998) for latent optimisation. NGD can be seen as an approximate second-order optimisation method (Pascanu & Bengio, 2013; Martens, 2014), and has been applied successfully in many domains. By using the positive semidefinite (PSD) Gauss-Newton matrix to approximate the (possibly negative definite) Hessian, NGD often works even better than exact second-order methods. NGD is expensive in high dimensional parameter spaces, even with approximations (Martens, 2014). However, we demonstrate it is efficient for latent optimisation, even in very large models. + +Given the gradient of $z$ , $\begin{array} { r } { g = \frac { \partial f ( z ) } { \partial z } } \end{array}$ ∂f(z)∂z , NGD computes the update as + +$$ +\Delta z = \alpha { \cal F } ^ { - 1 } g +$$ + +where the Fisher information matrix $F$ is defined as + +$$ +F = \mathbb { E } _ { p ( t \mid z ) } \left[ \nabla \ln p ( t | z ) \nabla \ln p ( t | z ) ^ { T } \right] +$$ + +The log-likelihood function $\ln { p ( t | z ) }$ typically corresponds to commonly used error functions such as cross entropy loss. This correspondence is not necessary when NGD is interpreted as an approximate second-order method, as has long been used in practice (Martens, 2014). Nevertheless, Appendix C provides a Poisson log-likelihood interpretation for the hinge loss commonly used in GANs (Lim & Ye, 2017; Tran et al., 2017). An important difference between latent optimisation and commonly seen senarios using NGD is that the expectation over the condition $( z )$ is absent. Since each $z$ is only responsible for generating one image, it only minimises the loss $L _ { G } ( z )$ for this particular instance. Computing per-sample Fisher this way is necessary to approximate SGA (see Appendix B.1 for details). + +More specifically, we use the empirical Fisher $F ^ { \prime }$ with Tikhonov damping, as in TONGA (Roux et al., 2008) + +$$ +F ^ { \prime } = g \cdot g ^ { T } + \beta I +$$ + +$F ^ { \prime }$ is cheaper to compute compared with the full Fisher, since $g$ is already available. The damping factor $\beta$ regularises the step size, which is important when $F ^ { \prime }$ only poorly approximates the Hessian + +![](images/2966b36cc9a244e4c3fd95bf4642683a3a97459d514a30b50a2e05c51b72cc21.jpg) +Figure 5: (a) The change from $\Delta z$ across training, in $D$ ’s output space and $z$ ’s Euclidean space. The distances are normalised by their standard derivations computed from a moving window of size 20 (1007 data points in total). (b) Training curves from models with different “stop gradient” operations. For reference, the training curve from an unablated model is plotted as the dashed line. All instances with stop gradient collapsed (FID went up) early in training. + +or when the Hessian changes too much across the step. Using the Sherman-Morrison formula, the NGD update can be simplified into the following closed form: + +$$ +\Delta z = \alpha \left( \frac { I } { \beta } - \frac { g g ^ { T } } { \beta ^ { 2 } + \beta g ^ { T } g } \right) g = \frac { \alpha } { \beta } \left( 1 - \frac { \| g \| ^ { 2 } } { \beta + \| g \| ^ { 2 } } \right) g +$$ + +which does not involve any matrix inversion. Thus, NGD adapts the step size according to the curvature estimate $\begin{array} { r } { c = \frac { 1 } { \beta } \left( 1 - \frac { \| g \| ^ { 2 } } { \beta + \| g \| ^ { 2 } } \right) } \end{array}$ . Figure ${ \textbf { 4 a } }$ illustrates the scaling for different values of $\beta$ . NGD automatically smooths the scale of updates by down-scaling the gradients as their norm grows, which also contributes to the smoothed norms of updates (Figure $4 \ \mathbf { b }$ ). Since the NGD update remains proportional to $g$ , our analysis based on gradient descent in section 3 still holds. + +# 5 EXPERIMENTS AND ANALYSIS + +We focus on large scale GANs based on BigGAN-deep (Brock et al., 2018) trained on $1 2 8 \times 1 2 8$ size images from the ImageNet dataset (Deng et al., 2009). In Appendix E, we present results from applying our algorithm on Spectral Normalised GANs trained with CIFAR dataset (Krizhevsky et al., 2009), which obtains state-of-the-art scores on this model. + +# 5.1 MODEL CONFIGURATION + +We used the standard BigGAN-deep architecture with three minor modifications: 1. We increased the size of the latent source from 128 to 256, to compensate the randomness of the source lost when optimising $z$ . 2. We use the uniform distribution $\mathcal { U } ( - 1 , 1 )$ instead of the standard normal distribution $\mathcal { N } ( 0 , 1 )$ for $p ( z )$ , to be consistent with the clipping operation (Algorithm 1). 3. We use leaky ReLU instead of ReLU as the non-linearity for smoother gradient flow for $\frac { \partial f ( z ) } { \partial z }$ . + +Consistent with detailed findings in Brock et al. (2018) that these changes have limited effect, our experiment with this baseline model obtains only slightly better scores compared with those in Brock et al. (2018) (Table 1, see also Figure 8). The FID and IS are computed as in Brock et al. (2018), and IS values are computed from checkpoints with the lowest FIDs. The means and standard deviations are computed from 5 models with different random seeds. + +To apply latent optimisation, we use a damping factor $\beta = 5 . 0$ combined with a large step size of $\alpha = 0 . 9$ . As an additional way of damping, we only optimise $5 0 \%$ of $z$ ’s dimensions. Optimising the entire population of $z$ was unstable in our experiments. Similar to $\mathbf { W } \mathbf { u }$ et al. (2019), we found it was helpful to regularise the Euclidean norm of weight-change $\Delta z$ , with a regulariser weight of + +300.0. All other hyper-parameters, including learning rates and a large batch size of 2048, remain the same as in BigGAN-deep; we did not optimise these hyper-parameters. We call this model LOGAN (NGD). + +# 5.2 BASIC RESULTS + +Employing the same architecture and number of parameters as the BigGAN-deep baseline, LOGAN (NGD) achieved better FID and IS (Table 1). As observed by Brock et al. (2018), BigGAN training always eventually collapsed. Training with LOGAN also collapsed, perhaps due to higher-order dynamics beyond the scope we have analysed, but took significantly longer (600k steps versus $3 0 0 \mathrm { k }$ steps with BigGAN-deep). + +During training, LOGAN was $2 - 3$ times slower per step compared with BigGAN-deep because of the additional forward and backward pass. We found that optimising $z$ during evaluation did not improve sample scores (even up to 10 steps), so we do not optimise $z$ for evaluation. Therefore, LOGAN has the same evaluation cost as original BigGAN-deep. To help understand this behaviour, we plot the change from $\Delta z$ during training in Figure 5 a. Although the movement in Euclidean space $| | \Delta z | |$ grew until training collapsed, the movement in $D$ ’s output space, measured as $\| f ( z + \Delta z ) - f ( z ) \|$ , remained unchanged (see Appendix $\mathrm { D }$ for details). As shown in our analysis, optimising $z$ improves the training dynamics, so LOGANs work well after training without requiring latent optimisation. + +# 5.3 ABLATION STUDIES + +We verify our theoretical analysis in section 3 by examining key components of Algorithm 1 via ablation studies. First, we experimented with using basic GD to optimising $z$ , as in Wu et al. (2019), and call this model LOGAN (GD). A smaller step size of $\alpha = 0 . 0 0 0 1$ was required; larger values were unstable and led to premature collapse of training. As shown in Table 1, the scores from LOGAN (GD) were worse than LOGAN (NGD) and similar to the baseline model. + +We then evaluate the effects of removing those terms depending on the ordinary gradient (eq. 3). Since these terms were computed $\frac { \partial f ( z ) } { \partial z }$ in eq. 8, which are not inback-propagating through the latent optimisation procedure, we removed them by selectively blocking back-propagation with “stop gradient” operations (e.g., in TensorFlow Abadi et al. 2016). Figure ${ \bf 5 \ B }$ shows the change of FIDs for the three models corresponding to removing $\left( \frac { \partial \Delta z } { \partial \theta _ { G } } \right) ^ { T } \ \frac { \partial f ( z ^ { \prime } ) } { \partial z ^ { \prime } }$ , removing $\begin{array} { r } { \left( \frac { \partial \Delta z } { \partial \theta _ { D } } \right) ^ { T } \frac { \partial f ( z ^ { \prime } ) } { \partial z ^ { \prime } } } \end{array}$ and removing both terms. As predicted by our analysis (section 3), both terms help stabilise training; training diverged early for all three ablations. + +# 5.4 TRUNCATION AND SAMPLES + +Truncation is a technique introduced by Brock et al. (2018) to illustrate the trade-off between the FID and IS in a trained model. For a model trained with $z \sim p ( z )$ from a source distribution symmetric around 0, such as the standard normal distribution $\mathcal { N } ( 0 , 1 )$ and the uniform distribution $\mathcal { U } ( - 1 , 1 )$ , down-scaling (truncating) the source $\bar { z } = s \cdot z$ with $0 \leq s \leq 1$ gives samples with higher visual quality but reduced diversity. This observation is quantified as higher IS and lower FID when evaluating samples from truncated distributions. + +Figure $^ { 3 \mathrm { ~ b ~ } }$ plots the truncation curves for the baseline BigGAN-deep model, LOGAN (GD) and LOGAN (NGD), obtained by varying the truncation (value of $s$ ) from 1.0 (no truncation, upper-left ends of the curves) to 0.02 (extreme truncation, bottom-right ends). Each curve shows the trade-off between FID and IS for an individual model; curves towards the upper-right corner indicate better overall sample quality. The relative positions of curves in Figure 3 (b) shows LOGAN (NGD) has the best sample quality. Interestingly, although LOGAN (GD) and the baseline model have similar scores without truncation (upper-left ends of the curves, see also Table 1), LOGAN (GD) was better behaved with increasing truncation, suggesting LOGAN (GD) still converged to a better equilibrium. For further reference, we plot truncation curves from additional baseline models in Figure 8. + +Figure 1 and Figure 2 show samples from chosen points on the truncation curves. In the high IS domain, C and D on the truncation curves both have similarly high IS of near 260. Samples from batches with such high IS have almost photo-realistic image quality. Figure 1 show that while the baseline model produced nearly uniform samples, LOGAN (NGD) could still generate highly diverse samples. On the other hand, A and B from Figure $^ { 3 \mathrm { ~ b ~ } }$ have similarly low FID of near 5, indicating high sample diversity. Samples in Figure $^ { 2 \mathbf { b } }$ show higher quality compared with those in a (e.g., the interfaces between the elephants and ground, the contours around the pandas). + +# 6 CONCLUSION + +In this work we present the LOGAN model which significantly improves the state-of-the-art on large scale GAN training for image generation by online optimising the latent source $z$ . Our results illustrate improvements in quantitative evaluation and samples with higher quality and diversity. Moreover, our analysis suggests that LOGAN fundamentally improves adversarial training dynamics. 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In particular, we show how the algorithm brings together ideas from symplectic gradient adjustment, unrolled GANs and stochastic approximation with two time scales. + +# B.1 APPROXIMATE SYMPLECTIC GRADIENT ADJUSTMENT + +To analyse LOGAN as a differentiable game we treat the latent step $\Delta z$ as adding a third player to the original game played by the discriminator and generator. The third player’s parameter, $\Delta z$ , is optimised online for each $z \sim p ( z )$ . Together the three players (latent player, discriminator, and generator) have losses averaged over a batch of samples: + +$$ +L = [ \eta L _ { G } , L _ { D } , L _ { G } ] ^ { T } +$$ + +where $\begin{array} { r } { \eta \ : = \ : \frac { 1 } { N } } \end{array}$ ( $N$ is the batch size) reflects the fact that each $\Delta z$ is only optimised for a single sample $z$ , so its contribution to the total loss across a batch is small compared with $\theta _ { D }$ and $\theta _ { G }$ which are directly optimised for batch losses. This choice of $\eta$ is essential for the following derivation, and has important practical implication. It means that the per-sample loss $L _ { G } ( z ^ { \prime } )$ , instead of the loss summed over a batch Therefore, when usin $\textstyle \sum _ { n = 1 } ^ { N } L _ { G } ( z _ { n } ^ { \prime } )$ , should be the only loss function guiding latent optimisation.ent descent (Section 4), the Fisher information matrix should only be computed using the current sample $z$ . + +The resulting simultaneous gradient is + +$$ +\begin{array} { r } { g = \left[ \eta \frac { \partial L _ { G } ( z ^ { \prime } ) } { \partial \Delta z } , \frac { \partial L _ { D } ( z ^ { \prime } ) } { \partial \theta _ { D } } , \frac { \partial L _ { G } ( z ^ { \prime } ) } { \partial \theta _ { G } } \right] ^ { T } = \left[ - \eta \frac { \partial f ( z ^ { \prime } ) } { \partial \Delta z } , \frac { \partial f ( z ^ { \prime } ) } { \partial \theta _ { D } } , - \frac { \partial f ( z ^ { \prime } ) } { \partial \theta _ { G } } \right] ^ { T } } \end{array} +$$ + +Following Balduzzi et al. (2018), we can write the Hessian of the game as: + +$$ +H = \left[ \begin{array} { c c c } { - \eta \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \Delta z ^ { 2 } } } & { - \eta \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \Delta z \partial \theta _ { D } } } & { - \eta \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \Delta z \partial \theta _ { G } } } \\ { \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \theta _ { D } \partial \Delta z } } & { \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \theta _ { D } ^ { 2 } } } & { \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \theta _ { D } \partial \theta _ { G } } } \\ { - \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \theta _ { G } \partial \Delta z } } & { - \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \theta _ { G } \partial \theta _ { D } } } & { - \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \theta _ { G } ^ { 2 } } } \end{array} \right] +$$ + +The presence of a non-zero anti-symmetric component in the Hessian + +$$ +A = \frac { 1 } { 2 } ( H - H ^ { T } ) = \left[ \begin{array} { c c c } { 0 } & { - \frac { 1 + \eta } { 2 } \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \Delta z \partial \theta _ { D } } } & { \frac { 1 - \eta } { 2 } \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \Delta z \partial \theta _ { G } } } \\ { \frac { 1 + \eta } { 2 } \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \theta _ { D } \partial \Delta z } } & { 0 } & { \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \theta _ { D } \partial \theta _ { G } } } \\ { - \frac { 1 - \eta } { 2 } \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \theta _ { G } \partial \Delta z } } & { - \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial \theta _ { G } \partial \theta _ { D } } } & { 0 } \end{array} \right] +$$ + +implies the dynamics have a rotational component which can cause cycling or slow down convergence. Since $\eta \ll 1$ for typical batch sizes (e.g., $\frac { 1 } { 6 4 }$ for DCGAN and $\scriptstyle { \frac { 1 } { 2 0 4 8 } }$ for BigGAN-deep), we abbreviate $\begin{array} { r } { \gamma = \frac { 1 + \eta } { 2 } \approx \frac { 1 - \eta } { 2 } } \end{array}$ 1−η2 to simplify notations. + +Symplectic gradient adjustment (SGA) counteracts the rotational force by adding an adjustment term to the gradient to obtain $g ^ { * } g + \lambda A ^ { T } g$ , which for the discriminator and generator has the form: + +$$ +\begin{array} { r l } & { g _ { D } ^ { * } = \cfrac { \partial f ( \boldsymbol { z } ^ { \prime } ) } { \partial \theta _ { D } } + \lambda \gamma \left( \cfrac { \partial ^ { 2 } f ( \boldsymbol { z } ^ { \prime } ) } { \partial \Delta \boldsymbol { z } \partial \theta _ { D } } \right) ^ { T } \cfrac { \partial f ( \boldsymbol { z } ^ { \prime } ) } { \partial \Delta \boldsymbol { z } } + \lambda \left( \cfrac { \partial ^ { 2 } f ( \boldsymbol { z } ^ { \prime } ) } { \partial \theta _ { G } \partial \theta _ { D } } \right) ^ { T } \cfrac { \partial f ( \boldsymbol { z } ^ { \prime } ) } { \partial \theta _ { G } } } \\ & { g _ { G } ^ { * } = - \cfrac { \partial f ( \boldsymbol { z } ^ { \prime } ) } { \partial \theta _ { G } } - \lambda \gamma \left( \cfrac { \partial ^ { 2 } f ( \boldsymbol { z } ^ { \prime } ) } { \partial \Delta \boldsymbol { z } \partial \theta _ { G } } \right) ^ { T } \cfrac { \partial f ( \boldsymbol { z } ^ { \prime } ) } { \partial \Delta \boldsymbol { z } } + \lambda \left( \cfrac { \partial f ( \boldsymbol { z } ^ { \prime } ) } { \partial \theta _ { D } \partial \theta _ { G } } \right) ^ { T } \cfrac { \partial f ( \boldsymbol { z } ^ { \prime } ) } { \partial \theta _ { D } } } \end{array} +$$ + +The gradient with respect to $\Delta z$ is ignored since the convergence of training only depends on $\theta _ { D }$ and $\theta _ { G }$ . + +If we drop the last terms in eq.17 and 18, which are expensive to compute for large models with high-dimensional $\theta _ { D }$ and $\theta _ { G }$ , and use $\begin{array} { r } { \frac { \partial f ( z ^ { \prime } ) } { \partial \Delta z } = \frac { \partial f ( z ^ { \prime } ) } { \partial z ^ { \prime } } } \end{array}$ , the adjusted updates can be rewritten as + +$$ +\begin{array} { l } { { g _ { D } ^ { * } \approx { \displaystyle \frac { \partial f ( z ^ { \prime } ) } { \partial \theta _ { D } } } + \lambda \gamma ~ \left( { \displaystyle \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial z ^ { \prime } \partial \theta _ { D } } } \right) ^ { T } ~ { \displaystyle \frac { \partial f ( z ^ { \prime } ) } { \partial z ^ { \prime } } } } } \\ { { g _ { G } ^ { * } \approx - { \displaystyle \frac { \partial f ( z ^ { \prime } ) } { \partial \theta _ { G } } } - \lambda \gamma ~ \left( { \displaystyle \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial z ^ { \prime } \partial \theta _ { G } } } \right) ^ { T } ~ { \displaystyle \frac { \partial f ( z ^ { \prime } ) } { \partial z ^ { \prime } } } } } \end{array} +$$ + +Because of the thiciently computing r, thand still the terms depend on is non-trivial (e.g., Pearl $\frac { \partial f ( z ^ { \prime } ) } { \partial z ^ { \prime } }$ to adjust the gradients. Effi- 1994). However, if we intro$\frac { \partial ^ { 2 } f ( \boldsymbol { z } ^ { \prime } ) } { \partial \boldsymbol { z } ^ { \prime } \partial \theta _ { D } }$ +duce the local approximation + +$$ +\frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial z ^ { \prime } \partial \theta _ { D } } \approx \frac { \partial ^ { 2 } f ( z ) } { \partial z \partial \theta _ { D } } \qquad \frac { \partial ^ { 2 } f ( z ^ { \prime } ) } { \partial z ^ { \prime } \partial \theta _ { D } } \approx \frac { \partial ^ { 2 } f ( z ) } { \partial z \partial \theta _ { D } } +$$ + +hen the adjusted gradient becomes identical to 8 from latent optimisation. + +In other words, automatic differentiation by commonly used machine learning packages can compute the adjusted gradient for $\theta _ { D }$ and $\theta _ { G }$ when back-propagating through the latent optimisation process. Despite the approximation involved in this analysis, both our experiments in section 5 and the results from Wu et al. (2019) verified that latent optimisation can significantly improve GAN training. + +# B.2 RELATION WITH UNROLLED GANS + +Latent optimisation can be seen as unrolling GANs (Metz et al., 2016) in the space of the latent, rather than the parameters. Unrolling in the latent space has the advantages that: + +1. LOGAN is more scalable than Unrolled GANs because it avoids second-order derivatives over a potentially very large number of parameters. +2. While unrolling the update of $D$ only affects the parameters of $G$ (as in Metz et al. 2016), latent optimisation effects both $D$ and $G$ as shown in eq. 8. + +We next formally present this connection by showing that SGA can be seen as approximating Unrolled GANs (Metz et al., 2016). For the update $\theta _ { D } ^ { \prime } = \theta _ { D } + \Delta \theta _ { D }$ , we have the Taylor expansion approximation at $\theta _ { D }$ : + +$$ +f ( z ; \theta _ { D } + \Delta \theta _ { D } , \theta _ { G } ) \approx f ( z ; \theta _ { D } , \theta _ { G } ) + \left( \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { D } } \right) ^ { T } \Delta \theta _ { D } +$$ + +Substitute $\begin{array} { r } { \Delta \theta _ { D } = - \alpha \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { D } } } \end{array}$ α ∂f(z;θD,θG) , and take the derivatives with respect to θG on both sides: + +$$ +\frac { \partial f ( z ; \theta _ { D } + \Delta \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } } \approx \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } } - 2 \alpha \left( \frac { \partial ^ { 2 } f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { D } \partial \theta _ { G } } \right) ^ { T } \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { D } } +$$ + +which is the same as eq. 18 (taking the negative sign). Compared with the exact gradient from the unroll: + +$$ +\frac { \partial f ( z ; \theta _ { D } + \Delta \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } } = \frac { \partial f ( z ; \theta _ { D } ^ { \prime } , \theta _ { G } ) } { \partial \theta _ { G } } - 2 \alpha \left( \frac { \partial ^ { 2 } f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { D } \partial \theta _ { G } } \right) ^ { T } \frac { \partial f ( z ; \theta _ { D } ^ { \prime } , \theta _ { G } ) } { \partial ( \theta _ { D } ^ { \prime } ) } +$$ + +The approximation in eq. 23 comes from using $\begin{array} { r l r } { \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { D } } } & { { } \approx } & { \frac { \partial f ( z ; \theta _ { D } ^ { \prime } , \theta _ { G } ) } { \partial \theta _ { D } ^ { \prime } } } \end{array}$ and $\begin{array} { r } { \frac { \partial f ( \boldsymbol { z } ; \boldsymbol { \theta } _ { D } , \boldsymbol { \theta } _ { G } ) } { \partial \boldsymbol { \theta } _ { G } } \approx } \end{array}$ $\frac { \partial f ( \boldsymbol { z } ; \boldsymbol { \theta } _ { D } ^ { \prime } , \boldsymbol { \theta } _ { G } ) } { \partial \boldsymbol { \theta } _ { G } }$ as a result of the linear approximation. + +At this point, unrolling $D$ update only affects $\theta _ { D }$ . Although it is expensive to unroll both $D$ and $G$ , in principle, we can unroll $G$ update and compute the gradient of $\theta _ { D }$ similarly using $\Delta \theta _ { G } =$ $\alpha \frac { \partial f ( z ; \mathbf { \bar { \theta } } _ { D } , \theta _ { G } ) } { \partial \theta _ { G } }$ ： + +$$ +\frac { \partial f ( z ; \theta _ { D } , \theta _ { G } + \Delta \theta _ { G } ) } { \partial \theta _ { D } } \approx \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { D } } + 2 \alpha \left( \frac { \partial ^ { 2 } f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } \partial \theta _ { D } } \right) ^ { T } \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } } +$$ + +which gives us the same update rule as SGA (eq. 17). This correspondence based on first order Taylor expansion is unsurprising, as SGA is based on linearising the adversarial dynamics (Balduzzi et al., 2018). + +# B.3 STOCHASTIC APPROXIMATION WITH TWO TIME SCALES + +Heusel et al. (2017) used the theory of stochastic approximation to analyse GAN training. Viewing the training process as stochastic approximation with two time scales (Borkar, 1997; Konda & Borkar, 1999), they suggest that the update of $D$ should be fast enough compared with that of $G$ . Under mild assumptions, Heusel et al. (2017) proved that such two time-scale update converges to local Nash equilibrium. Their analysis follows the idea of $( \tau , \delta )$ perturbation (Hirsch, 1989), where the slow updates $( G )$ is interpreted as a small perturbation over the ODE describing the fast update $( D )$ . Importantly, the size of perturbation $\delta$ is measured in the magnitude of parameter change, which is affected by both the learning rate and gradients. + +Here we show that LOGAN accelerates discriminator updates and slows down generator updates, thus helping the convergence of discriminator according to Heusel et al. (2017). We start from analysing the change of $\theta _ { G }$ . We assume that, without LO, it takes $\Delta \theta _ { G } = \theta _ { G } ^ { \prime } - \theta _ { G }$ to make a small constant amount of reduction in loss $L _ { G }$ : + +$$ +\rho = - f ( z ; \theta _ { D } , \theta _ { G } + \Delta \theta _ { G } ) + f ( z ; \theta _ { D } , \theta _ { G } ) +$$ + +Now using the optimised $z ^ { \prime } = z + \Delta z$ , we assess the change $\delta \theta _ { G }$ required to achieve the same amount of reduction: + +$$ +\rho = - f ( z + \Delta z ; \theta _ { D } , \theta _ { G } + \delta \theta _ { G } ) + f ( z ; \theta _ { D } , \theta _ { G } ) +$$ + +Intuitively, when $z$ “helps” $\theta _ { G }$ to achieve the same goal of increasing $f ( z ; \theta _ { D } , \theta _ { G } )$ by $\rho$ , the responsible of $\theta _ { G }$ becomes smaller, so it does not need to change as much as $\Delta \theta _ { G }$ , thus $\lVert \delta \theta _ { G } \rVert < \lVert \Delta \theta _ { G } \rVert$ . + +Formally, $f ( z ; \theta _ { D } , \theta _ { G } )$ and $f ( z + \Delta ; \theta _ { D } , \theta _ { G } + \delta \theta _ { G } )$ have the following Taylor expansions around $z$ and $\theta _ { G }$ : + +$$ +\begin{array} { c } { { f ( z ; \theta _ { d } , \theta _ { G } + \delta \theta _ { G } ) = f ( z ; \theta _ { D } , \theta _ { G } ) + \displaystyle \left( \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } } \right) ^ { T } \Delta \theta _ { G } + \epsilon ( \Delta \theta _ { G } ) } } \\ { { f ( z + \Delta z ; \theta _ { d } , \theta _ { G } + \delta \theta _ { G } ) = f ( z ; \theta _ { D } , \theta _ { G } ) + \displaystyle \left( \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial z } \right) ^ { T } } } \\ { { \Delta z + \displaystyle \left( \frac { \partial f ( z + \Delta z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } } \right) ^ { T } \delta \theta _ { G } + \epsilon ( \Delta z , \delta \theta _ { G } ) } } \end{array} +$$ + +Where $\epsilon ( \cdot )$ ’s are higher order terms of the increments. Using the assumption of eq. 26 and 27, we can combine eq. 28 and 29: + +$$ +\left( \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } } \right) ^ { T } \Delta \theta _ { G } = \left( \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial z } \right) ^ { T } \Delta z + \left( \frac { \partial f ( z + \Delta z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } } \right) ^ { T } \delta \theta _ { G } + \epsilon +$$ + +where $\epsilon = \epsilon ( \Delta z , \delta \theta _ { G } ) - \epsilon ( \Delta \theta _ { G } )$ . Since ∂f(z;θD,θG)∂z in gradient descent (eq. 3), + +$$ +\frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial z } \Delta z > 0 +$$ + +Therefore, we have the inequality + +$$ +\left( \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } } \right) ^ { T } \Delta \theta _ { G } < \left( \frac { \partial f ( z + \Delta z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } } \right) ^ { T } \delta \theta _ { G } + \epsilon +$$ + +If we further assume $\Delta \theta _ { G }$ and $\delta \theta _ { G }$ are obtained from stochastic gradient descent with identical learning rate, + +$$ +\Delta \theta _ { G } = \alpha \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } } \qquad \delta \theta _ { G } = \alpha \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { G } } +$$ + +substituting eq. 33 into eq. 32 gives + +$$ +\lVert \Delta \theta _ { G } \rVert < \lVert \delta \theta _ { G } \rVert + \epsilon +$$ + +The same analysis applies to the discriminator. The similar intuition is that it takes the discriminator additional effort to compensate the exploitation from the optimised $z ^ { \prime }$ . We then obtain + +$$ +\left( \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { D } } \right) ^ { T } \Delta \theta _ { D } = \left( \frac { \partial f ( z ; \theta _ { D } , \theta _ { G } ) } { \partial z } \right) ^ { T } \Delta z + \left( \frac { \partial f ( z + \Delta z ; \theta _ { D } , \theta _ { G } ) } { \partial \theta _ { D } } \right) ^ { T } \delta \theta _ { D } + \epsilon +$$ + +However, since the adversarial loss $L _ { D } = - L _ { G }$ , we have $\begin{array} { r } { \Delta \theta _ { D } = - \alpha \frac { \partial f ( \boldsymbol { z } ; \boldsymbol { \theta } _ { D } , \boldsymbol { \theta } _ { G } ) } { \partial \boldsymbol { \theta } _ { D } } } \end{array}$ and $\delta \theta _ { D } =$ $\begin{array} { r } { - \alpha \frac { \partial f ( \boldsymbol { z } ; \boldsymbol { \theta } _ { D } , \boldsymbol { \theta } _ { G } ) } { \partial \boldsymbol { \theta } _ { D } } } \end{array}$ taking the opposite signs of eq.33. For sufficiently small $\Delta z$ , $\Delta \theta _ { G }$ and $\delta \theta _ { G }$ , $\epsilon$ is close to zero, so $\lVert \Delta \theta _ { D } \rVert < \lVert \delta \theta _ { D } \rVert$ under our assumptions of small $\Delta z , \Delta \theta _ { G }$ and $\delta \theta _ { G }$ . + +mportantly, the bigger the product . Moreover, bigger step increases $\frac { \partial f ( z ) } { \partial z } \Delta z$ is, the more robust the id gap between updating qual and is to the error from, further facilitating $\epsilon$ $\mathbf { D }$ $\mathbf { G }$ convergence according to Heusel et al. (2017). Overall, our analysis suggests: + +1. More than one gradient descent step may not be helpful, since $\Delta z$ from multiple GD steps may deviate from the direction of $\frac { \partial f ( z ) } { \partial z }$ . +2. Large step of $\Delta z$ is more helpful in facilitating convergence by widening the gap between $\mathbf { D }$ and $\mathbf { G }$ updates (Heusel et al., 2017). +3. However, the step of $\Delta z$ cannot be too large. In addition to the linear approximation we used throughout our analysis, the approximate SGA breaks down when eq.21 is strongly violated when “overshoot” brings the gradients at $\frac { \partial f ( z ^ { \prime } ) } { \partial z ^ { \prime } }$ to the opposite sign of $\frac { \partial f ( z ) } { \partial z }$ . + +# C POISSON LIKELIHOOD FROM HINGE LOSS + +Here we provide a probabilistic interpretation of the hinge loss for the generator, which leads naturally to the scenario of a family of discriminators. Although this interpretation is not necessary for our current algorithm, it may provides useful guidance for incorporating multiple discriminators. + +We introduce the label $t = 1$ for real data and $t = 0$ fake samples. This section shows that the generator hinge loss + +$$ +L _ { G } = - D \left( G ( z ) \right) +$$ + +can be interpreted as a negative log-likelihood function: + +$$ +L _ { G } = - \ln p ( t = 1 ; D , G ( z ) ) +$$ + +Here $p ( t = 1 ; z , D , G )$ is the probability that the generated image $G ( z )$ can fool the discriminator $D$ . + +The original GAN’s discriminator can be interpreted as outputting a Bernoulli distribution $p ( t ; \beta _ { G } ) \mathbf { \bar { \alpha } } = \mathbf { \alpha } \beta _ { G } ^ { t } \cdot ( 1 - \beta _ { G } ) ^ { 1 - t }$ . In this case, if we parameterise $\beta _ { G } \ \bar { = } \ D \left( G ( z ) \right)$ , the generator loss is the negative log-likelihood + +$$ +- \ln P \big ( t = 1 ; D , G ( z ) \big ) = - \ln p ( t = 1 ; \beta _ { G } ) = - \ln \beta _ { G } = - \ln D \left( G ( z ) \right) +$$ + +Bernoulli, however, is not the only valid choice as the discriminator’s output distribution. Instead of sampling “1” or $ { { } ^ { 6 } } { 0 ^ { 9 } }$ , we assume that there are many identical discriminators that can independently vote to reject an input sample as fake. The number of votes $k$ in a given interval can be described by a Poisson distribution with parameter $\lambda$ with the following PMF: + +$$ +p ( k ; \lambda ) = \frac { \lambda ^ { k } e ^ { - \lambda } } { k ! } +$$ + +The probability that a generated image can fool all the discriminators is the probability of $G ( z )$ receiving no vote for rejection + +$$ +p ( k = 0 ; \lambda ) = e ^ { - \lambda } +$$ + +Therefore, we have the following negative log-likelihood as the generator loss if we parameterise $\lambda = - D \left( G ( z ) \right)$ : + +$$ +- \ln p \big ( k = 0 ; D , G ( z ) \big ) = - \ln p ( k = 0 ; \lambda ) = - D \left( G ( z ) \right) +$$ + +This interpretation has a caveat that when $D \left( G ( z ) \right) > 0$ the Poisson distribution is not well defined. However, in general the discriminator’s hinge loss + +$$ +{ \cal L } _ { D } = - \operatorname * { m i n } \left( 0 , - 1 + D ( x ) \right) - \operatorname * { m i n } \left( 0 , - 1 - D ( G ( z ) ) \right) +$$ + +pushes $D \left( G ( z ) \right) < 0$ via training. + +# D DETAILS IN COMPUTING DISTANCES IN FIGURE 5 A + +For a temporal sequence $x _ { 1 } , x _ { 2 } , \ldots , x _ { T }$ (changes of $z$ or $f ( z )$ at each training step in this paper), to normalise its variance while accounting for the non-stationarity, we process it as follows. We first compute the moving average and standard deviation over a window of size $N$ : + +$$ +\begin{array} { l } { \displaystyle \mu _ { t } = \frac { 1 } { N } \sum _ { u = t } ^ { t + N - 1 } x _ { u } } \\ { \displaystyle \sigma _ { t } = \sqrt { \frac { 1 } { N - 1 } \sum _ { u = t } ^ { t + N - 1 } ( x _ { u } - \mu _ { u } ) ^ { 2 } } } \end{array} +$$ + +Then normalise the sequence as: + +$$ +\bar { x } _ { t } = \frac { x _ { t } } { \sigma _ { t } } +$$ + +The result in Figure ${ \bf 5 a }$ is robust to the choice of window size. Our experiments with $N$ from 10 to 50 yielded visually similar plots. + +# E EXPERIMENTS WITH DCGAN AND CIFAR + +To test if latent optimisation works with models at more moderate scales, we applied it on SN-GANs (Miyato et al., 2018). Although our experiments on this model are less thorough than in the main paper with BigGAN-deep, we hope to provide basic guidelines for researchers interested in applying latent optimisation on smaller models. + +The experiments follows the same basic setup and hyper-parameter settings as the CS-GAN in Wu et al. (2019). There is no class conditioning in this model. For NGD, we found a smaller damping factor $\beta = 0 . 1$ , a $\| z \|$ regulariser weight of 3.0 (the same as in $\mathbf { W } \mathbf { u }$ et al. 2019), combined with optimising $7 0 \%$ of the latent source (instead of $5 0 \%$ for BigGAN-deep) worked best for SN-GANs. + +In addition, we found running extra latent optimisation steps benefited evaluation, so we use ten steps of latent optimisation in evaluation for results in this section, although the models were still trained with a single optimisation step. We reckon that smaller models might not be “over-parametrised” enough to fully amortise the computation from optimising $z$ , which can then further exploit the architecture in evaluation time. On the other hand, the overhead from running multiple iterations of latent optimisation is relatively small at this scale. We aim to further investigate this difference in future studies. + +Table 2 shows the FID and IS alongside SN-GAN and CS-CAN which used the same architecture. Here we observe similarly significant improvement over the baseline SN-GAN model, with an improvement of $1 6 . 8 \%$ in IS and $3 9 . 6 \%$ in FID. Figure 9 shows random samples from these two models. Overall, samples from LOGAN (NGD) have higher contrasts and sharper contours. + +Table 2: Comparison of Scores. The first and second columns are reproduced from Miyato et al. (2018) and Wu et al. (2019) respectively. We report the Inception Score (IS, higher is better, Salimans et al. 2016) and Frechet Inception Distance (FID, lower is better, Heusel et al. 2017). ´ + +
SN-GANCS-GANLOGAN (NGD)
FID29.323.1 ± 0.517.7 ± 0.4
IS7.42 ± 0.087.80 ± 0.058.67 ± 0.05
+ +![](images/08d18f774fc587387bb21732661c7ffc3db922b57aa6143398a3beb197685e05.jpg) +Figure 6: Samples from BigGAN-deep (a) and LOGAN (b) with the similarly high inception scores. Samples from the two panels were draw from truncations correspond to points C, D in figure $^ { 3 \mathrm { ~ b ~ } }$ respectively. (FID/IS: (a) 27.97/259.4, (b) 8.19/259.9) + +![](images/85eb8fa1823f783151421751466d469565435d09556bb7dbba3499f3ec9b9f32.jpg) +Figure 7: Samples from BigGAN-deep (a) and LOGAN (b) with the similarly low FID. Samples from the two panels were draw from truncations correspond to points A, B in figure $^ { 3 } \mathbf { b }$ respectively. (FID/IS: (a) 5.04/126.8, (b) 5.09/217.0) + +![](images/a84700ae275e2a00511145cb295e953cda39609b11d83381e9b2f310aeed347e.jpg) +Figure 8: Truncation curves with additional baselines. In addition to the truncation curves reported in Figure $^ { 3 \mathrm { ~ b ~ } }$ , here we also include the Spectral-Normalised GAN (Miyato et al., 2018), SelfAttention GAN (Zhang et al., 2019), original BigGAN and BigGAN-deep as presented in Brock et al. (2018). + +![](images/da1f330a00f9fc880d248896003a11028638743649f1581001989eb4a8c5c081.jpg) +Figure 9: (a) Samples from SN-GAN. (b) Samples from LOGAN. \ No newline at end of file diff --git a/parse/train/rJeU_1SFvr/rJeU_1SFvr_content_list.json b/parse/train/rJeU_1SFvr/rJeU_1SFvr_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..569c3936fff7c47d2c5cf69aafba0e0012e45aa8 --- /dev/null +++ b/parse/train/rJeU_1SFvr/rJeU_1SFvr_content_list.json @@ -0,0 +1,2381 @@ +[ + { + "type": "text", + "text": "LOGAN: LATENT OPTIMISATION FOR GENERATIVEADVERSARIAL NETWORKS", + "text_level": 1, + "bbox": [ + 176, + 98, + 823, + 146 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Anonymous authors Paper under double-blind review ", + "bbox": [ + 183, + 171, + 398, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 236, + 544, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Training generative adversarial networks requires balancing of delicate adversarial dynamics. Even with careful tuning, training may diverge or end up in a bad equilibrium with dropped modes. In this work, we introduce a new form of latent optimisation inspired by the CS-GAN and show that it improves adversarial dynamics by enhancing interactions between the discriminator and the generator. We develop supporting theoretical analysis from the perspectives of differentiable games and stochastic approximation. Our experiments demonstrate that latent optimisation can significantly improve GAN training, obtaining state-of-the-art performance for the ImageNet $1 2 8 \\times 1 2 8 )$ dataset. Our model achieves an Inception Score (IS) of 148 and an Frechet Inception Distance (FID) of ´ 3.4, an improvement of $1 7 \\%$ and $3 2 \\%$ in IS and FID respectively, compared with the baseline BigGAN-deep model with the same architecture and number of parameters. ", + "bbox": [ + 233, + 266, + 764, + 433 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 459, + 336, + 476 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generative Adversarial Nets (GANs) are implicit generative models that can be trained to match a given data distribution. GANs were originally proposed and demonstrated for images by Goodfellow et al. (2014). As the field of generative modelling has advanced, GANs have remained at the frontier, generating high-fidelity images at large scale (Brock et al., 2018). However, despite growing insights into the dynamics of GAN training, most recent advances in large-scale image generation come from architectural improvements (Radford et al., 2015; Zhang et al., 2019), or regularisation focusing on particular parts of the model (Miyato et al., 2018; Miyato & Koyama, 2018). Inspired by the compressed sensing GAN (CS-GAN; Wu et al., 2019), we further exploit the benefit of latent optimisation in adversarial games using natural gradient descent to optimise the latent variable $z$ at each step of training, presenting a scalable and easy to implement approach to improve the dynamical interaction between the discriminator and the generator. For clarity, we unify these approaches as latent optimised GANs (LOGAN). ", + "bbox": [ + 174, + 491, + 825, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To summarise our contributions: ", + "bbox": [ + 176, + 665, + 387, + 679 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. We present a novel analysis of latent optimisation in GANs from the perspective of differentiable games and stochastic approximation (Balduzzi et al., 2018; Heusel et al., 2017), arguing that latent optimisation can improve the dynamics of adversarial training. 2. Motivated by this analysis, we improve latent optimisation by taking advantage of efficient second-order updates. 3. Our algorithm improves the state-of-the-art BigGAN-deep model (Brock et al., 2018) by a significant margin, without introducing any architectural change or additional parameters, resulting in higher quality images and more diverse samples (Figure 1 and 2). ", + "bbox": [ + 212, + 690, + 825, + 814 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2 BACKGROUND ", + "text_level": 1, + "bbox": [ + 174, + 837, + 326, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2.1 NOTATION ", + "text_level": 1, + "bbox": [ + 174, + 869, + 287, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We use $\\theta _ { D }$ and $\\theta _ { G }$ to denote the vectors representing parameters of the generator and discriminator. We use $x$ for images, and $z$ for the latent source generating an image. The prime 0 is used to denote ", + "bbox": [ + 176, + 895, + 823, + 924 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/940acc1b2137ed3db28ecc22572b29ae004f7f4763b437aab5109fd2ff070819.jpg", + "image_caption": [ + "Figure 1: Samples from BigGAN-deep (a) and LOGAN (b) with similarly high IS. Samples from the two panels were drawn from truncation levels corresponding to points C and D in figure $^ { 3 \\mathrm { ~ b ~ } }$ respectively. (FID/IS: (a) 27.97/259.4, (b) 8.19/259.9) " + ], + "image_footnote": [], + "bbox": [ + 187, + 101, + 805, + 311 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/86601a8a9e19d78392a2f54a737be755f53742c748082b3e5d2bcc4246e83a01.jpg", + "image_caption": [ + "Figure 2: Samples from BigGAN-deep (a) and LOGAN (b) with similarly low FID. Samples from the two panels were drawn from truncation levels corresponding to points A and $\\mathbf { B }$ in figure $^ { 3 \\mathrm { ~ b ~ } }$ respectively. (FID/IS: (a) 5.04/126.8, (b) 5.09/217.0) " + ], + "image_footnote": [], + "bbox": [ + 183, + 382, + 813, + 637 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "a variable after one update step, e.g., $\\begin{array} { r } { \\theta _ { D } ^ { \\prime } = \\theta _ { D } - \\alpha \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { D } } } \\end{array}$ . $p ( x )$ and $p ( z )$ denote the data distribution and source distribution respectively. $\\mathbb { E } _ { p ( x ) } \\left[ f ( x ) \\right]$ indicates taking the expectation of function $f ( x )$ over the distribution $p ( x )$ . ", + "bbox": [ + 173, + 723, + 826, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2 GENERATIVE ADVERSARIAL NETS ", + "text_level": 1, + "bbox": [ + 176, + 795, + 455, + 809 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A GAN consists of a generator that generates image $x = G ( z ; \\theta _ { G } )$ from a latent source $z \\sim p ( z )$ , and a discriminator that scores the generated images as $D ( x ; \\theta _ { D } )$ (Goodfellow et al., 2014). Training GANs involves an adversarial game: while the discriminator tries to distinguish generated samples $x = G \\left( z ; \\theta _ { G } \\right)$ from data $x \\sim p ( x )$ , the generator tries to fool the discriminator. This procedure can be summarised as the following min-max game: ", + "bbox": [ + 173, + 821, + 825, + 893 + ], + "page_idx": 1 + }, + { + "type": "equation", + "img_path": "images/49ef6ac3aa97a2050826c51eaedc2251718eabbf84d8767c066a07fb39e16ce6.jpg", + "text": "$$\n\\operatorname* { m i n } _ { \\theta _ { D } } \\operatorname* { m a x } _ { \\theta _ { G } } \\mathbb { E } _ { z \\sim p ( x ) } [ h _ { D } ( D ( x ; \\theta _ { D } ) ) ] + \\mathbb { E } _ { z \\sim p ( z ) } [ h _ { G } ( D ( G ( z ; \\theta _ { G } ) ; \\theta _ { D } ) ) ]\n$$", + "text_format": "latex", + "bbox": [ + 264, + 904, + 735, + 928 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/b0a285d0b11e1f95e3558f73431b445e8ae14eb47fc99bd1352d736e2370866f.jpg", + "table_caption": [ + "Table 1: Comparison of model scores. BigGAN-deep results are reproduced from Brock et al. (2018). “baseline” indicates our reproduced BigGAN-deep with small modifications. The 3rd and 4th columns are from the gradient descent (GD, ablated) and natural gradient descent (NGD) versions of LOGAN respectively. We report the Inception Score (IS, higher is better, Salimans et al. 2016) and Frechet Inception Distance (FID, lower is better, Heusel et al. 2017). ´ " + ], + "table_footnote": [], + "table_body": "
BigGAN-DeepbaselineLOGAN (GD)LOGAN (NGD)
FID5.7 ± 0.34.92±0.054.86±0.093.36± 0.14
IS124.5 ± 2.0126.6 ± 1.3127.7 ± 3.5148.2 ±3.1
", + "bbox": [ + 245, + 186, + 746, + 232 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The exact form of $h ( \\cdot )$ depends on the choice of loss function (Goodfellow et al., 2014; Arjovsky et al., 2017; Nowozin et al., 2016). To simplify our presentation and analysis, we use the Wasserstein loss (Arjovsky et al., 2017), so that $h _ { D } ( t ) = - t$ and $h _ { G } ( t ) = t$ . Our experiments with BigGANdeep uses the hinge loss (Lim & Ye, 2017; Tran et al., 2017), which is identical to this form in its linear regime. Our analysis can be generalised to other losses as in previous theoretical work (e.g., Arora et al. 2017). To simplify notation, we abbreviate $f ( z ; \\theta _ { D } , \\bar { \\theta _ { G } } ) = D \\left( G \\left( z ; \\theta _ { G } \\right) ; \\theta _ { D } \\right)$ , which may be further simplified as $f ( z )$ when the explicit dependency on $\\theta _ { D }$ and $\\theta _ { G }$ can be omitted. ", + "bbox": [ + 173, + 260, + 825, + 359 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Training GANs requires carefully balancing updates to $D$ and $G$ , and is sensitive to both architecture and algorithm choices (Salimans et al., 2016; Radford et al., 2015). A recent milestone is BigGAN (and BigGAN-deep, Brock et al. 2018), which pushed the boundary of high fidelity image generation by scaling up GANs to an unprecedented level. BigGANs use an architecture based on residual blocks (He et al., 2016), in combination with regularisation mechanisms and self-attention (Saxe et al., 2014; Miyato et al., 2018; Zhang et al., 2019). ", + "bbox": [ + 173, + 364, + 825, + 449 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here we aim to improve the adversarial dynamics during training. We focus on the second term in eq. 1 which is at the heart of the min-max game, with adversarial losses for $D$ and $G$ , which can be written as ", + "bbox": [ + 173, + 455, + 823, + 494 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/d9798381816ebb13030f282630c2560b31a3f074b0b634f6a5b39ac9d25df4d5.jpg", + "text": "$$\nL ( z ) = \\left[ L _ { D } ( z ) , L _ { G } ( z ) \\right] ^ { T } = \\left[ f ( z ) , - f ( z ) \\right] ^ { T }\n$$", + "text_format": "latex", + "bbox": [ + 352, + 492, + 647, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Computing the gradients with respect to $\\theta _ { D }$ and $\\theta _ { G }$ obtains the following gradient, which cannot be expressed as the gradient of any single function (Balduzzi et al., 2018): ", + "bbox": [ + 174, + 520, + 825, + 549 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/ba041598a8041667fbb96c46986d1a22e659d254c76784899c8f385f41c5eb9e.jpg", + "text": "$$\ng = \\left[ \\frac { \\partial L _ { D } ( z ) } { \\partial \\theta _ { D } } , \\frac { \\partial L _ { G } ( z ) } { \\partial \\theta _ { G } } \\right] ^ { T } = \\left[ \\frac { \\partial f ( z ) } { \\partial \\theta _ { D } } , - \\frac { \\partial f ( z ) } { \\partial \\theta _ { G } } \\right] ^ { T }\n$$", + "text_format": "latex", + "bbox": [ + 328, + 565, + 668, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The fact that $g$ is not the gradient of a function implies that gradient updates in GANs can exhibit cycling behaviour which can slow down or prevent convergence. In Balduzzi et al. (2018), vector fields of this form are referred to as the simultaneous gradient. Although many GAN models use alternating update rules (e.g., Goodfellow et al. 2014; Brock et al. 2018), following the gradient with respect to $\\theta _ { D }$ and $\\theta _ { G }$ alternatively in each step, they can still suffer from cycling, so we use the simpler simultaneous gradient (eq. 3) for our analysis. ", + "bbox": [ + 174, + 603, + 825, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3 LATENT OPTIMISED GANS ", + "text_level": 1, + "bbox": [ + 176, + 702, + 403, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by compressed sensing (Candes et al., 2006; Donoho, 2006), Wu et al. (2019) introduced latent optimisation for GANs. We call this type of model latent-optimised GANs (LOGAN). Latent optimization has been shown to improve the stability of training as well as the final performance for medium-sized models such as DCGANs and Spectral Normalised GANs (Radford et al., 2015; Miyato et al., 2018). Latent optimisation exploits knowledge from $D$ to guide updates of $z$ . Intuitively, the gradient $\\begin{array} { r } { \\nabla _ { z } f ( z ) = \\frac { \\partial f ( z ) } { \\partial z } } \\end{array}$ points in the direction that satisfies the discriminator $D$ , which implies better samples. Therefore, instead of using the randomly sampled $z \\sim p ( z )$ , Wu et al. (2019) uses the optimised latent ", + "bbox": [ + 173, + 727, + 825, + 842 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/688128d9a5c94b3de1956cd3f8bdcb92f13470f5607bb114da55974e7e2c77ce.jpg", + "text": "$$\n\\Delta z = \\alpha \\frac { \\partial f ( z ) } { \\partial z } \\qquad z ^ { \\prime } = z + \\Delta z\n$$", + "text_format": "latex", + "bbox": [ + 388, + 840, + 611, + 871 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in eq. 1 for training 1. The general algorithm is summarised in Algorithm 1 and illustrated in Figure 3 a. We develop the natural gradient descent form of latent update in Section 4. ", + "bbox": [ + 176, + 873, + 823, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c24ba41202d98dd0cfb864fbd092fb035f3fe4c84763666ad586e37a8cf9c30d.jpg", + "image_caption": [ + "Figure 3: (a) Schematic of LOGAN. We first compute a forward pass through $G$ and $D$ with a sampled latent $z$ . Then, gradients from the generator loss (dashed red arrow) are used to compute an improved latent, $z ^ { \\prime }$ . After this optimised latent code is used in a second forward pass, we compute gradients of the discriminator back through the latent optimisation into the model parameters $\\theta _ { D }$ , $\\theta _ { G }$ . These gradients are used to update the model. (b) Truncation curves illustrate the FID/IS tradeoff for each model by altering the range of the noise source $p ( z )$ . GD: gradient descent. NGD: natural gradient descent. Points A, B, C, D correspond to samples shown in Figure 1 and 2. " + ], + "image_footnote": [], + "bbox": [ + 186, + 103, + 805, + 351 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/7621bc68cbafac60b0d64ace1b03ec6acb5884420b7f0434eb4545e4cce8ef75.jpg", + "table_caption": [ + "Algorithm 1 Latent Optimised GANs with Automatic Differentiation " + ], + "table_footnote": [], + "table_body": "
Input: data distribution p(x),latent distribution p(z),D(:; 0D), G(-; 0g),learning rate α, batch size N repeat
Initialise discriminator and generator parameters 0D,0G fori=1 to Ndo
Sample z ~ p(z),x~p(x)
Compute the gradient D(G(z)) and use it to obtain △z from eq. 4 (GD) or eq. 12 (NGD) dz
Optimise the latent z' ← [+ △z],[:] indicates clipping the value between -1 and 1
= -D(G(z))
D(G(z'))-D(x) end for
Compute batch losses LG =N∑i=11 JN (i) and LD=∑=1 N L(i) LD
aLD aLG Update 0D and 0G with the gradients
0D， G
until reaches the maximum training steps
", + "bbox": [ + 178, + 493, + 820, + 708 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3 ANALYSIS OF THE ALGORITHM ", + "text_level": 1, + "bbox": [ + 176, + 734, + 467, + 751 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To understand how latent optimisation improves GAN training, we analyse LOGAN as a 2-player differentiable game following Balduzzi et al. (2018); Gemp & Mahadevan (2018); Letcher et al. (2019). The appendix provides a complementary analysis that relates LOGAN to unrolled GANs (Metz et al., 2016) and stochastic approximation (Heusel et al., 2017; Borkar, 1997). ", + "bbox": [ + 173, + 767, + 825, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1 THE SYMPLECTIC GRADIENT ADJUSTMENT (SGA) ", + "text_level": 1, + "bbox": [ + 173, + 840, + 571, + 856 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "An important problem with gradient-based optimization in GANs is that the vector-field generated by the losses of the discriminator and generator is not a gradient vector field. It follows that gradient descent is not guaranteed to find a local optimum and can cycle, which can slow down convergence or lead to phenomena like mode collapse and mode hopping. Balduzzi et al. (2018); Gemp & ", + "bbox": [ + 174, + 867, + 825, + 924 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mahadevan (2018) proposed Symplectic Gradient Adjustment (SGA) to improve the dynamics of gradient-based methods in adversarial games. For a game with gradient $g$ (eq. 3), define the Hessian as the second order derivatives with respect to the parameters, $H = \\nabla _ { \\theta } g$ . SGA uses the adjusted gradient ", + "bbox": [ + 173, + 103, + 825, + 159 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/2f712f91570b8cabf50bafb2c9192f40a2b4dd9910cc127fcc455f6eab5db2b9.jpg", + "text": "$$\ng ^ { * } = g + \\lambda A ^ { T } g \\quad { \\mathrm { w h e r e ~ } } \\lambda { \\mathrm { ~ i s ~ a ~ p o s i t i v e ~ c o n s t a n t } }\n$$", + "text_format": "latex", + "bbox": [ + 334, + 157, + 665, + 176 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and $\\begin{array} { r } { A = \\frac 1 2 ( H - H ^ { T } ) } \\end{array}$ is the anti-symmetric component of the Hessian. Applying SGA to GANs yields the adjusted updates (see Appendix B.1 for details): ", + "bbox": [ + 173, + 179, + 823, + 208 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/67e0d1e919fcd9d52a6a4d1e8c4bf0b6635f27b2e19aa29369320e597bd75929.jpg", + "text": "$$\ng ^ { \\ast } = \\left[ \\frac { \\partial f ( z ) } { \\partial \\theta _ { D } } + \\lambda \\left( \\frac { \\partial ^ { 2 } f ( z ) } { \\partial \\theta _ { G } \\partial \\theta _ { D } } \\right) ^ { T } \\frac { \\partial f ( z ) } { \\partial \\theta _ { G } } , - \\frac { \\partial f ( z ) } { \\partial \\theta _ { G } } + \\lambda \\left( \\frac { \\partial ^ { 2 } f ( z ) } { \\partial \\theta _ { D } \\partial \\theta _ { G } } \\right) ^ { T } \\frac { \\partial f ( z ) } { \\partial \\theta _ { D } } \\right] ^ { T }\n$$", + "text_format": "latex", + "bbox": [ + 217, + 213, + 779, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compared with $g$ in eq. 3, the adjusted gradient $g ^ { * }$ has second-order terms reflecting the interactions between $D$ and $G$ . SGA has been shown to significantly improve GAN training in basic examples (Balduzzi et al., 2018), allowing faster and more robust convergence to stable fixed points (local Nash equilibria). Unfortunately, SGA is expensive to scale because computing the second-order derivatives with respect to all parameters is expensive. ", + "bbox": [ + 173, + 262, + 825, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Explicitly computing the gradients for the discriminator and generator at $z ^ { \\prime }$ after one step of latent optimisation (eq. 4) obtains ", + "bbox": [ + 173, + 339, + 823, + 367 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/ae331ab67c9eb164e4a2a09e560c8a52fe1b2f6fc9dfda3a2ea49271b13a8f6d.jpg", + "text": "$$\n\\begin{array} { r l r } & { } & { \\left[ \\frac { d L _ { D } } { d \\theta _ { D } } , \\frac { d L _ { G } } { d \\theta _ { G } } \\right] } ^ { T } = { { \\left[ \\frac { \\partial f ( { \\boldsymbol { z } } ^ { \\prime } ) } { \\partial \\theta _ { D } } + \\left( \\frac { \\partial \\Delta { \\boldsymbol { z } } } { \\partial \\theta _ { D } } \\right) ^ { T } \\frac { \\partial f ( { \\boldsymbol { z } } ^ { \\prime } ) } { \\partial \\Delta { \\boldsymbol { z } } } , - \\frac { \\partial f ( { \\boldsymbol { z } } ^ { \\prime } ) } { \\partial \\theta _ { G } } - \\left( \\frac { \\partial \\Delta { \\boldsymbol { z } } } { \\partial \\theta _ { G } } \\right) ^ { T } \\frac { \\partial f ( { \\boldsymbol { z } } ^ { \\prime } ) } { \\partial \\Delta { \\boldsymbol { z } } } \\right] } ^ { T } { \\left( \\boldsymbol { \\hat { z } } ^ { \\prime } \\right) } } \\\\ & { } & { = { { \\left[ \\frac { \\partial f ( { \\boldsymbol { z } } ^ { \\prime } ) } { \\partial \\theta _ { D } } + \\alpha \\left( \\frac { \\partial ^ { 2 } f ( { \\boldsymbol { z } } ) } { \\partial \\boldsymbol { z } \\partial \\theta _ { D } } \\right) ^ { T } \\frac { \\partial f ( { \\boldsymbol { z } } ^ { \\prime } ) } { \\partial { \\boldsymbol { z } } ^ { \\prime } } , - \\frac { \\partial f ( { \\boldsymbol { z } } ^ { \\prime } ) } { \\partial \\theta _ { G } } - \\alpha \\left( \\frac { \\partial ^ { 2 } f ( { \\boldsymbol { z } } ) } { \\partial \\boldsymbol { z } \\partial \\theta _ { G } } \\right) ^ { T } \\frac { \\partial f ( { \\boldsymbol { z } } ^ { \\prime } ) } { \\partial { \\boldsymbol { z } } ^ { \\prime } } \\right] } ^ { T } } } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 183, + 372, + 812, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In both equations, the first terms represent how $f ( z ^ { \\prime } )$ depends on the parameters directly and the second terms represent how $f ( z ^ { \\prime } )$ depends on the parameters via the optimised latent source. For the second equality, we substitute $\\begin{array} { r } { \\Delta z = \\alpha \\frac { \\partial f ( z ) } { \\partial z } } \\end{array}$ as the gradient-based update of $z$ and use $\\begin{array} { r } { \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial \\Delta z } = } \\end{array}$ ∂f(z0)∂z0 . The original GAN’s gradient (eq. 3) does not include any second-order term, since ∆z = 0 without latent optimisation. In LOGAN, these extra terms are computed by automatic differentiation when back-propagating through the latent optimisation process (see Algorithm 1). ", + "bbox": [ + 173, + 484, + 825, + 579 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The SGA updates in eq. 6 and the LOGAN updates in eq. 8 are strikingly similar, suggesting that the latent step used by LOGAN reduces the negative effects of cycling by introducing a symplectic gradient adjustment into the optimization procedure. The role of the latent step can be formalized in terms of a third player, whose goal is to help the generator, see appendix B for details. ", + "bbox": [ + 174, + 584, + 825, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Crucially, latent optimisation approximates SGA using only second-order derivatives with respect to the latent $z$ and parameters of the discriminator and generator separately. The second order terms involving parameters of both the discriminator and the generator – which are extremely expensive to compute – are not used. For latent $z$ ’s with dimensions typically used in GANs (e.g., 128–256, orders of magnitude less than the number of parameters), these can be computed efficiently. In short, latent optimisation efficiently couples the gradients of the discriminator and generator, as prescribed by SGA, but using the much lower-dimensional latent source $z$ which makes the adjustment scalable. ", + "bbox": [ + 173, + 647, + 825, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "An important consequence of reducing the rotational aspect of GAN dynamics is that it is possible to use larger step sizes during training which suggests using stronger optimisers to fully take advantage of latent optimisation. Latent optimisation can improve GAN training dynamics further by allowing larger single steps $\\Delta z$ towards the direction of $\\frac { \\partial f ( z ) } { \\partial z }$ ) without overshooting. ", + "bbox": [ + 174, + 752, + 825, + 813 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2 UNROLLING AND STOCHASTIC APPROXIMATION ", + "text_level": 1, + "bbox": [ + 174, + 828, + 547, + 843 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Appendix B further explains how LOGAN relates to unrolled GANs (Metz et al., 2016) and stochastic approximation. Our main finding is that latent optimisation accelerates the speed of updating $D$ relative to that of $G$ , facilitating convergence according to Heusel et al. (2017) (see also Figure ${ } 4 \\mathbf { b }$ ). In particular, the generator requires less update compared with $D$ to achieve the same reduction of loss, because latent optimisation “helps” $G$ . ", + "bbox": [ + 174, + 853, + 825, + 924 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a79b2b3f2b5f754129923560fbb71709f81bf8416d83d1a5b7fe6082daa4985c.jpg", + "image_caption": [ + "Figure 4: (a) Scaling of gradients in natural gradient descent. We use $\\beta = 5$ in BigGAN-Deep experiments. (b) The update speed of the discriminator relative to the generator shown as the difference $\\lVert \\Delta \\boldsymbol { \\theta } _ { D } \\rVert - \\lVert \\Delta \\boldsymbol { \\theta } _ { G } \\rVert$ after each update step. Lines are smoothed with moving average using window size 20 (in total, there are 3007, 1659 and 1768 data points for each curve). For all curves oscillation strongly after training collapsed. " + ], + "image_footnote": [], + "bbox": [ + 191, + 101, + 803, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4 LOGAN WITH NATURAL GRADIENT DESCENT ", + "text_level": 1, + "bbox": [ + 173, + 401, + 596, + 417 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Although our analysis suggests using strong optimisers for optimising $z$ , Wu et al. (2019) only used basic gradient descent (GD) with a fixed step-size. This choice limits the size $\\Delta z$ can take: in order not to overshoot when the curvature is large, the step size would be too conservative when the curvature is small. We hypothesis that GD is more detrimental for larger models, which have complex loss surfaces with highly varying curvatures. Consistent with this hypothesis, we observed only marginal improvement over the baseline using GD (section 5.3, Table 1, Figure $3 \\mathbf { b }$ ). ", + "bbox": [ + 174, + 433, + 825, + 517 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this work, we instead use natural gradient descent (NGD, Amari 1998) for latent optimisation. NGD can be seen as an approximate second-order optimisation method (Pascanu & Bengio, 2013; Martens, 2014), and has been applied successfully in many domains. By using the positive semidefinite (PSD) Gauss-Newton matrix to approximate the (possibly negative definite) Hessian, NGD often works even better than exact second-order methods. NGD is expensive in high dimensional parameter spaces, even with approximations (Martens, 2014). However, we demonstrate it is efficient for latent optimisation, even in very large models. ", + "bbox": [ + 173, + 522, + 825, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Given the gradient of $z$ , $\\begin{array} { r } { g = \\frac { \\partial f ( z ) } { \\partial z } } \\end{array}$ ∂f(z)∂z , NGD computes the update as ", + "bbox": [ + 173, + 627, + 602, + 647 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/2c49f0b8b0f04b55a506116dd240c53aa29cbd4b6cfc4d69b7f74cd067ac65be.jpg", + "text": "$$\n\\Delta z = \\alpha { \\cal F } ^ { - 1 } g\n$$", + "text_format": "latex", + "bbox": [ + 447, + 651, + 550, + 670 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where the Fisher information matrix $F$ is defined as ", + "bbox": [ + 173, + 674, + 514, + 689 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/e0d8ff335b0f8f2887e74bbcf6734a13504dff62a18761803152f89d2faa4905.jpg", + "text": "$$\nF = \\mathbb { E } _ { p ( t \\mid z ) } \\left[ \\nabla \\ln p ( t | z ) \\nabla \\ln p ( t | z ) ^ { T } \\right]\n$$", + "text_format": "latex", + "bbox": [ + 370, + 693, + 625, + 713 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The log-likelihood function $\\ln { p ( t | z ) }$ typically corresponds to commonly used error functions such as cross entropy loss. This correspondence is not necessary when NGD is interpreted as an approximate second-order method, as has long been used in practice (Martens, 2014). Nevertheless, Appendix C provides a Poisson log-likelihood interpretation for the hinge loss commonly used in GANs (Lim & Ye, 2017; Tran et al., 2017). An important difference between latent optimisation and commonly seen senarios using NGD is that the expectation over the condition $( z )$ is absent. Since each $z$ is only responsible for generating one image, it only minimises the loss $L _ { G } ( z )$ for this particular instance. Computing per-sample Fisher this way is necessary to approximate SGA (see Appendix B.1 for details). ", + "bbox": [ + 173, + 717, + 825, + 843 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "More specifically, we use the empirical Fisher $F ^ { \\prime }$ with Tikhonov damping, as in TONGA (Roux et al., 2008) ", + "bbox": [ + 173, + 849, + 825, + 877 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/fe2012b5a63efe20a298e3446b3edb39108a3712d4a798b9d3788fd8fd48eb92.jpg", + "text": "$$\nF ^ { \\prime } = g \\cdot g ^ { T } + \\beta I\n$$", + "text_format": "latex", + "bbox": [ + 437, + 875, + 560, + 893 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$F ^ { \\prime }$ is cheaper to compute compared with the full Fisher, since $g$ is already available. The damping factor $\\beta$ regularises the step size, which is important when $F ^ { \\prime }$ only poorly approximates the Hessian ", + "bbox": [ + 173, + 895, + 825, + 924 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2966b36cc9a244e4c3fd95bf4642683a3a97459d514a30b50a2e05c51b72cc21.jpg", + "image_caption": [ + "Figure 5: (a) The change from $\\Delta z$ across training, in $D$ ’s output space and $z$ ’s Euclidean space. The distances are normalised by their standard derivations computed from a moving window of size 20 (1007 data points in total). (b) Training curves from models with different “stop gradient” operations. For reference, the training curve from an unablated model is plotted as the dashed line. All instances with stop gradient collapsed (FID went up) early in training. " + ], + "image_footnote": [], + "bbox": [ + 189, + 99, + 807, + 300 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "or when the Hessian changes too much across the step. Using the Sherman-Morrison formula, the NGD update can be simplified into the following closed form: ", + "bbox": [ + 173, + 407, + 821, + 435 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/85b1b200778700525fac67da4661c56a14ab82cd6d2e008688bb1863b8a5e21a.jpg", + "text": "$$\n\\Delta z = \\alpha \\left( \\frac { I } { \\beta } - \\frac { g g ^ { T } } { \\beta ^ { 2 } + \\beta g ^ { T } g } \\right) g = \\frac { \\alpha } { \\beta } \\left( 1 - \\frac { \\| g \\| ^ { 2 } } { \\beta + \\| g \\| ^ { 2 } } \\right) g\n$$", + "text_format": "latex", + "bbox": [ + 303, + 440, + 694, + 477 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "which does not involve any matrix inversion. Thus, NGD adapts the step size according to the curvature estimate $\\begin{array} { r } { c = \\frac { 1 } { \\beta } \\left( 1 - \\frac { \\| g \\| ^ { 2 } } { \\beta + \\| g \\| ^ { 2 } } \\right) } \\end{array}$ . Figure ${ \\textbf { 4 a } }$ illustrates the scaling for different values of $\\beta$ . NGD automatically smooths the scale of updates by down-scaling the gradients as their norm grows, which also contributes to the smoothed norms of updates (Figure $4 \\ \\mathbf { b }$ ). Since the NGD update remains proportional to $g$ , our analysis based on gradient descent in section 3 still holds. ", + "bbox": [ + 174, + 481, + 825, + 561 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5 EXPERIMENTS AND ANALYSIS ", + "text_level": 1, + "bbox": [ + 176, + 580, + 459, + 597 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We focus on large scale GANs based on BigGAN-deep (Brock et al., 2018) trained on $1 2 8 \\times 1 2 8$ size images from the ImageNet dataset (Deng et al., 2009). In Appendix E, we present results from applying our algorithm on Spectral Normalised GANs trained with CIFAR dataset (Krizhevsky et al., 2009), which obtains state-of-the-art scores on this model. ", + "bbox": [ + 174, + 611, + 825, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1 MODEL CONFIGURATION ", + "text_level": 1, + "bbox": [ + 174, + 684, + 390, + 699 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We used the standard BigGAN-deep architecture with three minor modifications: 1. We increased the size of the latent source from 128 to 256, to compensate the randomness of the source lost when optimising $z$ . 2. We use the uniform distribution $\\mathcal { U } ( - 1 , 1 )$ instead of the standard normal distribution $\\mathcal { N } ( 0 , 1 )$ for $p ( z )$ , to be consistent with the clipping operation (Algorithm 1). 3. We use leaky ReLU instead of ReLU as the non-linearity for smoother gradient flow for $\\frac { \\partial f ( z ) } { \\partial z }$ . ", + "bbox": [ + 174, + 710, + 825, + 785 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Consistent with detailed findings in Brock et al. (2018) that these changes have limited effect, our experiment with this baseline model obtains only slightly better scores compared with those in Brock et al. (2018) (Table 1, see also Figure 8). The FID and IS are computed as in Brock et al. (2018), and IS values are computed from checkpoints with the lowest FIDs. The means and standard deviations are computed from 5 models with different random seeds. ", + "bbox": [ + 173, + 790, + 825, + 861 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To apply latent optimisation, we use a damping factor $\\beta = 5 . 0$ combined with a large step size of $\\alpha = 0 . 9$ . As an additional way of damping, we only optimise $5 0 \\%$ of $z$ ’s dimensions. Optimising the entire population of $z$ was unstable in our experiments. Similar to $\\mathbf { W } \\mathbf { u }$ et al. (2019), we found it was helpful to regularise the Euclidean norm of weight-change $\\Delta z$ , with a regulariser weight of ", + "bbox": [ + 174, + 867, + 825, + 924 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "300.0. All other hyper-parameters, including learning rates and a large batch size of 2048, remain the same as in BigGAN-deep; we did not optimise these hyper-parameters. We call this model LOGAN (NGD). ", + "bbox": [ + 174, + 103, + 823, + 146 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2 BASIC RESULTS ", + "text_level": 1, + "bbox": [ + 174, + 170, + 326, + 184 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Employing the same architecture and number of parameters as the BigGAN-deep baseline, LOGAN (NGD) achieved better FID and IS (Table 1). As observed by Brock et al. (2018), BigGAN training always eventually collapsed. Training with LOGAN also collapsed, perhaps due to higher-order dynamics beyond the scope we have analysed, but took significantly longer (600k steps versus $3 0 0 \\mathrm { k }$ steps with BigGAN-deep). ", + "bbox": [ + 174, + 198, + 825, + 268 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "During training, LOGAN was $2 - 3$ times slower per step compared with BigGAN-deep because of the additional forward and backward pass. We found that optimising $z$ during evaluation did not improve sample scores (even up to 10 steps), so we do not optimise $z$ for evaluation. Therefore, LOGAN has the same evaluation cost as original BigGAN-deep. To help understand this behaviour, we plot the change from $\\Delta z$ during training in Figure 5 a. Although the movement in Euclidean space $| | \\Delta z | |$ grew until training collapsed, the movement in $D$ ’s output space, measured as $\\| f ( z + \\Delta z ) - f ( z ) \\|$ , remained unchanged (see Appendix $\\mathrm { D }$ for details). As shown in our analysis, optimising $z$ improves the training dynamics, so LOGANs work well after training without requiring latent optimisation. ", + "bbox": [ + 173, + 275, + 825, + 401 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3 ABLATION STUDIES ", + "text_level": 1, + "bbox": [ + 176, + 424, + 352, + 439 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We verify our theoretical analysis in section 3 by examining key components of Algorithm 1 via ablation studies. First, we experimented with using basic GD to optimising $z$ , as in Wu et al. (2019), and call this model LOGAN (GD). A smaller step size of $\\alpha = 0 . 0 0 0 1$ was required; larger values were unstable and led to premature collapse of training. As shown in Table 1, the scores from LOGAN (GD) were worse than LOGAN (NGD) and similar to the baseline model. ", + "bbox": [ + 174, + 453, + 825, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We then evaluate the effects of removing those terms depending on the ordinary gradient (eq. 3). Since these terms were computed $\\frac { \\partial f ( z ) } { \\partial z }$ in eq. 8, which are not inback-propagating through the latent optimisation procedure, we removed them by selectively blocking back-propagation with “stop gradient” operations (e.g., in TensorFlow Abadi et al. 2016). Figure ${ \\bf 5 \\ B }$ shows the change of FIDs for the three models corresponding to removing $\\left( \\frac { \\partial \\Delta z } { \\partial \\theta _ { G } } \\right) ^ { T } \\ \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } }$ , removing $\\begin{array} { r } { \\left( \\frac { \\partial \\Delta z } { \\partial \\theta _ { D } } \\right) ^ { T } \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } } } \\end{array}$ and removing both terms. As predicted by our analysis (section 3), both terms help stabilise training; training diverged early for all three ablations. ", + "bbox": [ + 173, + 530, + 825, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4 TRUNCATION AND SAMPLES ", + "text_level": 1, + "bbox": [ + 176, + 679, + 411, + 693 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Truncation is a technique introduced by Brock et al. (2018) to illustrate the trade-off between the FID and IS in a trained model. For a model trained with $z \\sim p ( z )$ from a source distribution symmetric around 0, such as the standard normal distribution $\\mathcal { N } ( 0 , 1 )$ and the uniform distribution $\\mathcal { U } ( - 1 , 1 )$ , down-scaling (truncating) the source $\\bar { z } = s \\cdot z$ with $0 \\leq s \\leq 1$ gives samples with higher visual quality but reduced diversity. This observation is quantified as higher IS and lower FID when evaluating samples from truncated distributions. ", + "bbox": [ + 174, + 708, + 825, + 791 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure $^ { 3 \\mathrm { ~ b ~ } }$ plots the truncation curves for the baseline BigGAN-deep model, LOGAN (GD) and LOGAN (NGD), obtained by varying the truncation (value of $s$ ) from 1.0 (no truncation, upper-left ends of the curves) to 0.02 (extreme truncation, bottom-right ends). Each curve shows the trade-off between FID and IS for an individual model; curves towards the upper-right corner indicate better overall sample quality. The relative positions of curves in Figure 3 (b) shows LOGAN (NGD) has the best sample quality. Interestingly, although LOGAN (GD) and the baseline model have similar scores without truncation (upper-left ends of the curves, see also Table 1), LOGAN (GD) was better behaved with increasing truncation, suggesting LOGAN (GD) still converged to a better equilibrium. For further reference, we plot truncation curves from additional baseline models in Figure 8. ", + "bbox": [ + 173, + 797, + 825, + 924 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 1 and Figure 2 show samples from chosen points on the truncation curves. In the high IS domain, C and D on the truncation curves both have similarly high IS of near 260. Samples from batches with such high IS have almost photo-realistic image quality. Figure 1 show that while the baseline model produced nearly uniform samples, LOGAN (NGD) could still generate highly diverse samples. On the other hand, A and B from Figure $^ { 3 \\mathrm { ~ b ~ } }$ have similarly low FID of near 5, indicating high sample diversity. Samples in Figure $^ { 2 \\mathbf { b } }$ show higher quality compared with those in a (e.g., the interfaces between the elephants and ground, the contours around the pandas). ", + "bbox": [ + 173, + 103, + 825, + 202 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6 CONCLUSION ", + "text_level": 1, + "bbox": [ + 174, + 220, + 318, + 237 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work we present the LOGAN model which significantly improves the state-of-the-art on large scale GAN training for image generation by online optimising the latent source $z$ . Our results illustrate improvements in quantitative evaluation and samples with higher quality and diversity. Moreover, our analysis suggests that LOGAN fundamentally improves adversarial training dynamics. We therefore expect our method to be useful in other tasks that involve adversarial training, including representation learning and inference (Donahue et al., 2017; Dumoulin et al., 2017), text generation (Zhang et al., 2019), style learning (Zhu et al., 2017; Karras et al., 2019), audio generation (Donahue et al., 2018) and video generation (Vondrick et al., 2016; Clark et al., 2019). ", + "bbox": [ + 173, + 252, + 825, + 364 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "REFERENCES ", + "text_level": 1, + "bbox": [ + 174, + 385, + 285, + 400 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Mart´ın Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Geoffrey Irving, Michael Isard, et al. Tensorflow: A system for largescale machine learning. 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In Proceedings of the IEEE international conference on computer vision, pp. 2223–2232, 2017. ", + "bbox": [ + 171, + 102, + 826, + 390 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "A ADDITIONAL SAMPLES AND RESULTS ", + "text_level": 1, + "bbox": [ + 176, + 414, + 526, + 430 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Figure 6 and 7 provide additional samples, organised similarly as in Figure 1 and 2. Figure 8 shows additional truncation curves. ", + "bbox": [ + 173, + 444, + 823, + 473 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "B DETAILED ANALYSIS OF LATENT OPTIMISATION ", + "text_level": 1, + "bbox": [ + 174, + 492, + 614, + 510 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "In this section we present three complementary analyses of LOGAN. In particular, we show how the algorithm brings together ideas from symplectic gradient adjustment, unrolled GANs and stochastic approximation with two time scales. ", + "bbox": [ + 174, + 523, + 825, + 565 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "B.1 APPROXIMATE SYMPLECTIC GRADIENT ADJUSTMENT ", + "text_level": 1, + "bbox": [ + 174, + 582, + 593, + 597 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "To analyse LOGAN as a differentiable game we treat the latent step $\\Delta z$ as adding a third player to the original game played by the discriminator and generator. The third player’s parameter, $\\Delta z$ , is optimised online for each $z \\sim p ( z )$ . Together the three players (latent player, discriminator, and generator) have losses averaged over a batch of samples: ", + "bbox": [ + 173, + 607, + 825, + 664 + ], + "page_idx": 10 + }, + { + "type": "equation", + "img_path": "images/3f634eef99021f2ea1d703ef6a70a926be391935e383b212b017baee8ba7da96.jpg", + "text": "$$\nL = [ \\eta L _ { G } , L _ { D } , L _ { G } ] ^ { T }\n$$", + "text_format": "latex", + "bbox": [ + 424, + 666, + 573, + 685 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "where $\\begin{array} { r } { \\eta \\ : = \\ : \\frac { 1 } { N } } \\end{array}$ ( $N$ is the batch size) reflects the fact that each $\\Delta z$ is only optimised for a single sample $z$ , so its contribution to the total loss across a batch is small compared with $\\theta _ { D }$ and $\\theta _ { G }$ which are directly optimised for batch losses. This choice of $\\eta$ is essential for the following derivation, and has important practical implication. It means that the per-sample loss $L _ { G } ( z ^ { \\prime } )$ , instead of the loss summed over a batch Therefore, when usin $\\textstyle \\sum _ { n = 1 } ^ { N } L _ { G } ( z _ { n } ^ { \\prime } )$ , should be the only loss function guiding latent optimisation.ent descent (Section 4), the Fisher information matrix should only be computed using the current sample $z$ . ", + "bbox": [ + 173, + 686, + 825, + 789 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "The resulting simultaneous gradient is ", + "bbox": [ + 176, + 795, + 426, + 810 + ], + "page_idx": 10 + }, + { + "type": "equation", + "img_path": "images/70e7fe009e5b1609bb818fa3772fc182835a16495fe562233928ba82814530ea.jpg", + "text": "$$\n\\begin{array} { r } { g = \\left[ \\eta \\frac { \\partial L _ { G } ( z ^ { \\prime } ) } { \\partial \\Delta z } , \\frac { \\partial L _ { D } ( z ^ { \\prime } ) } { \\partial \\theta _ { D } } , \\frac { \\partial L _ { G } ( z ^ { \\prime } ) } { \\partial \\theta _ { G } } \\right] ^ { T } = \\left[ - \\eta \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial \\Delta z } , \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial \\theta _ { D } } , - \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial \\theta _ { G } } \\right] ^ { T } } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 267, + 813, + 727, + 842 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Following Balduzzi et al. (2018), we can write the Hessian of the game as: ", + "bbox": [ + 174, + 844, + 663, + 858 + ], + "page_idx": 10 + }, + { + "type": "equation", + "img_path": "images/c1405e82f56815cd622ed4e0f107f458103a4d376f606efc461889292e473a2f.jpg", + "text": "$$\nH = \\left[ \\begin{array} { c c c } { - \\eta \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\Delta z ^ { 2 } } } & { - \\eta \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\Delta z \\partial \\theta _ { D } } } & { - \\eta \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\Delta z \\partial \\theta _ { G } } } \\\\ { \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\theta _ { D } \\partial \\Delta z } } & { \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\theta _ { D } ^ { 2 } } } & { \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\theta _ { D } \\partial \\theta _ { G } } } \\\\ { - \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\theta _ { G } \\partial \\Delta z } } & { - \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\theta _ { G } \\partial \\theta _ { D } } } & { - \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\theta _ { G } ^ { 2 } } } \\end{array} \\right]\n$$", + "text_format": "latex", + "bbox": [ + 338, + 861, + 656, + 929 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "The presence of a non-zero anti-symmetric component in the Hessian ", + "bbox": [ + 174, + 103, + 630, + 118 + ], + "page_idx": 11 + }, + { + "type": "equation", + "img_path": "images/06f68846debd7be03af0b8c45a25ad62e753ceedbbf6feeb7d863e75698a5519.jpg", + "text": "$$\nA = \\frac { 1 } { 2 } ( H - H ^ { T } ) = \\left[ \\begin{array} { c c c } { 0 } & { - \\frac { 1 + \\eta } { 2 } \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\Delta z \\partial \\theta _ { D } } } & { \\frac { 1 - \\eta } { 2 } \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\Delta z \\partial \\theta _ { G } } } \\\\ { \\frac { 1 + \\eta } { 2 } \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\theta _ { D } \\partial \\Delta z } } & { 0 } & { \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\theta _ { D } \\partial \\theta _ { G } } } \\\\ { - \\frac { 1 - \\eta } { 2 } \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\theta _ { G } \\partial \\Delta z } } & { - \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial \\theta _ { G } \\partial \\theta _ { D } } } & { 0 } \\end{array} \\right]\n$$", + "text_format": "latex", + "bbox": [ + 261, + 121, + 736, + 186 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "implies the dynamics have a rotational component which can cause cycling or slow down convergence. Since $\\eta \\ll 1$ for typical batch sizes (e.g., $\\frac { 1 } { 6 4 }$ for DCGAN and $\\scriptstyle { \\frac { 1 } { 2 0 4 8 } }$ for BigGAN-deep), we abbreviate $\\begin{array} { r } { \\gamma = \\frac { 1 + \\eta } { 2 } \\approx \\frac { 1 - \\eta } { 2 } } \\end{array}$ 1−η2 to simplify notations. ", + "bbox": [ + 176, + 188, + 820, + 234 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Symplectic gradient adjustment (SGA) counteracts the rotational force by adding an adjustment term to the gradient to obtain $g ^ { * } g + \\lambda A ^ { T } g$ , which for the discriminator and generator has the form: ", + "bbox": [ + 176, + 239, + 823, + 281 + ], + "page_idx": 11 + }, + { + "type": "equation", + "img_path": "images/f82a74d96af732845e2e2f6d32024d52311fa45b640f03a70427ce193a4974a0.jpg", + "text": "$$\n\\begin{array} { r l } & { g _ { D } ^ { * } = \\cfrac { \\partial f ( \\boldsymbol { z } ^ { \\prime } ) } { \\partial \\theta _ { D } } + \\lambda \\gamma \\left( \\cfrac { \\partial ^ { 2 } f ( \\boldsymbol { z } ^ { \\prime } ) } { \\partial \\Delta \\boldsymbol { z } \\partial \\theta _ { D } } \\right) ^ { T } \\cfrac { \\partial f ( \\boldsymbol { z } ^ { \\prime } ) } { \\partial \\Delta \\boldsymbol { z } } + \\lambda \\left( \\cfrac { \\partial ^ { 2 } f ( \\boldsymbol { z } ^ { \\prime } ) } { \\partial \\theta _ { G } \\partial \\theta _ { D } } \\right) ^ { T } \\cfrac { \\partial f ( \\boldsymbol { z } ^ { \\prime } ) } { \\partial \\theta _ { G } } } \\\\ & { g _ { G } ^ { * } = - \\cfrac { \\partial f ( \\boldsymbol { z } ^ { \\prime } ) } { \\partial \\theta _ { G } } - \\lambda \\gamma \\left( \\cfrac { \\partial ^ { 2 } f ( \\boldsymbol { z } ^ { \\prime } ) } { \\partial \\Delta \\boldsymbol { z } \\partial \\theta _ { G } } \\right) ^ { T } \\cfrac { \\partial f ( \\boldsymbol { z } ^ { \\prime } ) } { \\partial \\Delta \\boldsymbol { z } } + \\lambda \\left( \\cfrac { \\partial f ( \\boldsymbol { z } ^ { \\prime } ) } { \\partial \\theta _ { D } \\partial \\theta _ { G } } \\right) ^ { T } \\cfrac { \\partial f ( \\boldsymbol { z } ^ { \\prime } ) } { \\partial \\theta _ { D } } } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 253, + 281, + 738, + 359 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "The gradient with respect to $\\Delta z$ is ignored since the convergence of training only depends on $\\theta _ { D }$ and $\\theta _ { G }$ . ", + "bbox": [ + 174, + 361, + 823, + 390 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "If we drop the last terms in eq.17 and 18, which are expensive to compute for large models with high-dimensional $\\theta _ { D }$ and $\\theta _ { G }$ , and use $\\begin{array} { r } { \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial \\Delta z } = \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } } } \\end{array}$ , the adjusted updates can be rewritten as ", + "bbox": [ + 174, + 395, + 823, + 430 + ], + "page_idx": 11 + }, + { + "type": "equation", + "img_path": "images/ddd060faa830066b423a9dba1bf2398d1116d935be8c7b4059ae1347eff153f6.jpg", + "text": "$$\n\\begin{array} { l } { { g _ { D } ^ { * } \\approx { \\displaystyle \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial \\theta _ { D } } } + \\lambda \\gamma ~ \\left( { \\displaystyle \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } \\partial \\theta _ { D } } } \\right) ^ { T } ~ { \\displaystyle \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } } } } } \\\\ { { g _ { G } ^ { * } \\approx - { \\displaystyle \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial \\theta _ { G } } } - \\lambda \\gamma ~ \\left( { \\displaystyle \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } \\partial \\theta _ { G } } } \\right) ^ { T } ~ { \\displaystyle \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } } } } } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 351, + 433, + 645, + 511 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Because of the thiciently computing r, thand still the terms depend on is non-trivial (e.g., Pearl $\\frac { \\partial f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } }$ to adjust the gradients. Effi- 1994). However, if we intro$\\frac { \\partial ^ { 2 } f ( \\boldsymbol { z } ^ { \\prime } ) } { \\partial \\boldsymbol { z } ^ { \\prime } \\partial \\theta _ { D } }$ \nduce the local approximation ", + "bbox": [ + 173, + 513, + 823, + 564 + ], + "page_idx": 11 + }, + { + "type": "equation", + "img_path": "images/35cff76831eacae66e68db90fbb7ecc829f2cd7e044aab85a02fce6866b78817.jpg", + "text": "$$\n\\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } \\partial \\theta _ { D } } \\approx \\frac { \\partial ^ { 2 } f ( z ) } { \\partial z \\partial \\theta _ { D } } \\qquad \\frac { \\partial ^ { 2 } f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } \\partial \\theta _ { D } } \\approx \\frac { \\partial ^ { 2 } f ( z ) } { \\partial z \\partial \\theta _ { D } }\n$$", + "text_format": "latex", + "bbox": [ + 351, + 568, + 647, + 602 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "hen the adjusted gradient becomes identical to 8 from latent optimisation. ", + "bbox": [ + 186, + 603, + 655, + 618 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "In other words, automatic differentiation by commonly used machine learning packages can compute the adjusted gradient for $\\theta _ { D }$ and $\\theta _ { G }$ when back-propagating through the latent optimisation process. Despite the approximation involved in this analysis, both our experiments in section 5 and the results from Wu et al. (2019) verified that latent optimisation can significantly improve GAN training. ", + "bbox": [ + 173, + 625, + 825, + 694 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "B.2 RELATION WITH UNROLLED GANS ", + "text_level": 1, + "bbox": [ + 176, + 710, + 464, + 726 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Latent optimisation can be seen as unrolling GANs (Metz et al., 2016) in the space of the latent, rather than the parameters. Unrolling in the latent space has the advantages that: ", + "bbox": [ + 173, + 736, + 823, + 765 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "1. LOGAN is more scalable than Unrolled GANs because it avoids second-order derivatives over a potentially very large number of parameters. \n2. While unrolling the update of $D$ only affects the parameters of $G$ (as in Metz et al. 2016), latent optimisation effects both $D$ and $G$ as shown in eq. 8. ", + "bbox": [ + 210, + 775, + 825, + 837 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "We next formally present this connection by showing that SGA can be seen as approximating Unrolled GANs (Metz et al., 2016). For the update $\\theta _ { D } ^ { \\prime } = \\theta _ { D } + \\Delta \\theta _ { D }$ , we have the Taylor expansion approximation at $\\theta _ { D }$ : ", + "bbox": [ + 178, + 845, + 825, + 888 + ], + "page_idx": 11 + }, + { + "type": "equation", + "img_path": "images/78317d9d47e2549c887d661c5307f48b600bca77663bca33a556d3df5e6d0547.jpg", + "text": "$$\nf ( z ; \\theta _ { D } + \\Delta \\theta _ { D } , \\theta _ { G } ) \\approx f ( z ; \\theta _ { D } , \\theta _ { G } ) + \\left( \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { D } } \\right) ^ { T } \\Delta \\theta _ { D }\n$$", + "text_format": "latex", + "bbox": [ + 281, + 890, + 717, + 929 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Substitute $\\begin{array} { r } { \\Delta \\theta _ { D } = - \\alpha \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { D } } } \\end{array}$ α ∂f(z;θD,θG) , and take the derivatives with respect to θG on both sides: ", + "bbox": [ + 171, + 99, + 774, + 121 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/5b4757c45da4bce2b3b273adb772fefb3404f5732f9ff9bdc418fbd210ff275f.jpg", + "text": "$$\n\\frac { \\partial f ( z ; \\theta _ { D } + \\Delta \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } } \\approx \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } } - 2 \\alpha \\left( \\frac { \\partial ^ { 2 } f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { D } \\partial \\theta _ { G } } \\right) ^ { T } \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { D } }\n$$", + "text_format": "latex", + "bbox": [ + 205, + 127, + 763, + 165 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "which is the same as eq. 18 (taking the negative sign). Compared with the exact gradient from the unroll: ", + "bbox": [ + 173, + 170, + 826, + 198 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/b9c16173498b9a199f8317feb4362c7cd47d0a484904c103e6548a649ef4f32c.jpg", + "text": "$$\n\\frac { \\partial f ( z ; \\theta _ { D } + \\Delta \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } } = \\frac { \\partial f ( z ; \\theta _ { D } ^ { \\prime } , \\theta _ { G } ) } { \\partial \\theta _ { G } } - 2 \\alpha \\left( \\frac { \\partial ^ { 2 } f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { D } \\partial \\theta _ { G } } \\right) ^ { T } \\frac { \\partial f ( z ; \\theta _ { D } ^ { \\prime } , \\theta _ { G } ) } { \\partial ( \\theta _ { D } ^ { \\prime } ) }\n$$", + "text_format": "latex", + "bbox": [ + 207, + 202, + 764, + 241 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "The approximation in eq. 23 comes from using $\\begin{array} { r l r } { \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { D } } } & { { } \\approx } & { \\frac { \\partial f ( z ; \\theta _ { D } ^ { \\prime } , \\theta _ { G } ) } { \\partial \\theta _ { D } ^ { \\prime } } } \\end{array}$ and $\\begin{array} { r } { \\frac { \\partial f ( \\boldsymbol { z } ; \\boldsymbol { \\theta } _ { D } , \\boldsymbol { \\theta } _ { G } ) } { \\partial \\boldsymbol { \\theta } _ { G } } \\approx } \\end{array}$ $\\frac { \\partial f ( \\boldsymbol { z } ; \\boldsymbol { \\theta } _ { D } ^ { \\prime } , \\boldsymbol { \\theta } _ { G } ) } { \\partial \\boldsymbol { \\theta } _ { G } }$ as a result of the linear approximation. ", + "bbox": [ + 173, + 247, + 825, + 289 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "At this point, unrolling $D$ update only affects $\\theta _ { D }$ . Although it is expensive to unroll both $D$ and $G$ , in principle, we can unroll $G$ update and compute the gradient of $\\theta _ { D }$ similarly using $\\Delta \\theta _ { G } =$ $\\alpha \\frac { \\partial f ( z ; \\mathbf { \\bar { \\theta } } _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } }$ ： ", + "bbox": [ + 173, + 295, + 825, + 344 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/a13e4b99474e8adbcd85d8000d5b173696b338a4702f571b621bb4f994a41e82.jpg", + "text": "$$\n\\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } + \\Delta \\theta _ { G } ) } { \\partial \\theta _ { D } } \\approx \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { D } } + 2 \\alpha \\left( \\frac { \\partial ^ { 2 } f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } \\partial \\theta _ { D } } \\right) ^ { T } \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } }\n$$", + "text_format": "latex", + "bbox": [ + 209, + 349, + 763, + 388 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "which gives us the same update rule as SGA (eq. 17). This correspondence based on first order Taylor expansion is unsurprising, as SGA is based on linearising the adversarial dynamics (Balduzzi et al., 2018). ", + "bbox": [ + 173, + 393, + 823, + 435 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "B.3 STOCHASTIC APPROXIMATION WITH TWO TIME SCALES ", + "text_level": 1, + "bbox": [ + 173, + 452, + 609, + 467 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Heusel et al. (2017) used the theory of stochastic approximation to analyse GAN training. Viewing the training process as stochastic approximation with two time scales (Borkar, 1997; Konda & Borkar, 1999), they suggest that the update of $D$ should be fast enough compared with that of $G$ . Under mild assumptions, Heusel et al. (2017) proved that such two time-scale update converges to local Nash equilibrium. Their analysis follows the idea of $( \\tau , \\delta )$ perturbation (Hirsch, 1989), where the slow updates $( G )$ is interpreted as a small perturbation over the ODE describing the fast update $( D )$ . Importantly, the size of perturbation $\\delta$ is measured in the magnitude of parameter change, which is affected by both the learning rate and gradients. ", + "bbox": [ + 173, + 477, + 825, + 590 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Here we show that LOGAN accelerates discriminator updates and slows down generator updates, thus helping the convergence of discriminator according to Heusel et al. (2017). We start from analysing the change of $\\theta _ { G }$ . We assume that, without LO, it takes $\\Delta \\theta _ { G } = \\theta _ { G } ^ { \\prime } - \\theta _ { G }$ to make a small constant amount of reduction in loss $L _ { G }$ : ", + "bbox": [ + 173, + 595, + 825, + 654 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/560dd7ea33fa2ab6bac3edd07f29bfea53b60fb73c0da37564cef24388f6b7a8.jpg", + "text": "$$\n\\rho = - f ( z ; \\theta _ { D } , \\theta _ { G } + \\Delta \\theta _ { G } ) + f ( z ; \\theta _ { D } , \\theta _ { G } )\n$$", + "text_format": "latex", + "bbox": [ + 356, + 659, + 642, + 676 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Now using the optimised $z ^ { \\prime } = z + \\Delta z$ , we assess the change $\\delta \\theta _ { G }$ required to achieve the same amount of reduction: ", + "bbox": [ + 174, + 681, + 823, + 710 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/33bfe519ea27fb3cc07953789e04f99bf10855a41a6814d2c03e24d712738a29.jpg", + "text": "$$\n\\rho = - f ( z + \\Delta z ; \\theta _ { D } , \\theta _ { G } + \\delta \\theta _ { G } ) + f ( z ; \\theta _ { D } , \\theta _ { G } )\n$$", + "text_format": "latex", + "bbox": [ + 338, + 717, + 660, + 734 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Intuitively, when $z$ “helps” $\\theta _ { G }$ to achieve the same goal of increasing $f ( z ; \\theta _ { D } , \\theta _ { G } )$ by $\\rho$ , the responsible of $\\theta _ { G }$ becomes smaller, so it does not need to change as much as $\\Delta \\theta _ { G }$ , thus $\\lVert \\delta \\theta _ { G } \\rVert < \\lVert \\Delta \\theta _ { G } \\rVert$ . ", + "bbox": [ + 176, + 739, + 823, + 768 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Formally, $f ( z ; \\theta _ { D } , \\theta _ { G } )$ and $f ( z + \\Delta ; \\theta _ { D } , \\theta _ { G } + \\delta \\theta _ { G } )$ have the following Taylor expansions around $z$ and $\\theta _ { G }$ : ", + "bbox": [ + 173, + 773, + 825, + 804 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/b269fe998c4514bfe1f9b11591d16220b3c11dbcf589ae3d2036981f5c9a6899.jpg", + "text": "$$\n\\begin{array} { c } { { f ( z ; \\theta _ { d } , \\theta _ { G } + \\delta \\theta _ { G } ) = f ( z ; \\theta _ { D } , \\theta _ { G } ) + \\displaystyle \\left( \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } } \\right) ^ { T } \\Delta \\theta _ { G } + \\epsilon ( \\Delta \\theta _ { G } ) } } \\\\ { { f ( z + \\Delta z ; \\theta _ { d } , \\theta _ { G } + \\delta \\theta _ { G } ) = f ( z ; \\theta _ { D } , \\theta _ { G } ) + \\displaystyle \\left( \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial z } \\right) ^ { T } } } \\\\ { { \\Delta z + \\displaystyle \\left( \\frac { \\partial f ( z + \\Delta z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } } \\right) ^ { T } \\delta \\theta _ { G } + \\epsilon ( \\Delta z , \\delta \\theta _ { G } ) } } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 232, + 808, + 766, + 925 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Where $\\epsilon ( \\cdot )$ ’s are higher order terms of the increments. Using the assumption of eq. 26 and 27, we can combine eq. 28 and 29: ", + "bbox": [ + 173, + 103, + 825, + 132 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/eb0fbf8ff34caaf9e0785a7d90c0fe6e5c83db3aa8175fa714064e095a8226bd.jpg", + "text": "$$\n\\left( \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } } \\right) ^ { T } \\Delta \\theta _ { G } = \\left( \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial z } \\right) ^ { T } \\Delta z + \\left( \\frac { \\partial f ( z + \\Delta z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } } \\right) ^ { T } \\delta \\theta _ { G } + \\epsilon\n$$", + "text_format": "latex", + "bbox": [ + 184, + 138, + 790, + 176 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "where $\\epsilon = \\epsilon ( \\Delta z , \\delta \\theta _ { G } ) - \\epsilon ( \\Delta \\theta _ { G } )$ . Since ∂f(z;θD,θG)∂z in gradient descent (eq. 3), ", + "bbox": [ + 171, + 183, + 743, + 204 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/858f0c65d77db71a418a03d70c5e0606399c15898887cbb3f48e18b293dd0b98.jpg", + "text": "$$\n\\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial z } \\Delta z > 0\n$$", + "text_format": "latex", + "bbox": [ + 421, + 209, + 578, + 242 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Therefore, we have the inequality ", + "bbox": [ + 174, + 247, + 397, + 262 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/db5b604b7ec94cc6f59305cd5b5265121dd0c73f8e9d8c2c1896d27ffa48cca5.jpg", + "text": "$$\n\\left( \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } } \\right) ^ { T } \\Delta \\theta _ { G } < \\left( \\frac { \\partial f ( z + \\Delta z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } } \\right) ^ { T } \\delta \\theta _ { G } + \\epsilon\n$$", + "text_format": "latex", + "bbox": [ + 287, + 268, + 715, + 308 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "If we further assume $\\Delta \\theta _ { G }$ and $\\delta \\theta _ { G }$ are obtained from stochastic gradient descent with identical learning rate, ", + "bbox": [ + 173, + 313, + 823, + 340 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/5110787851e3c0737d7cb10dc05adb2764ab13cef0bde9dd05eedfdb6bf7ec2a.jpg", + "text": "$$\n\\Delta \\theta _ { G } = \\alpha \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } } \\qquad \\delta \\theta _ { G } = \\alpha \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { G } }\n$$", + "text_format": "latex", + "bbox": [ + 302, + 340, + 694, + 375 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "substituting eq. 33 into eq. 32 gives ", + "bbox": [ + 174, + 376, + 408, + 391 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/2756506a6e2ccfcb30acbeff91257cd388a2e6e75ab1615852a3ab6933c68f80.jpg", + "text": "$$\n\\lVert \\Delta \\theta _ { G } \\rVert < \\lVert \\delta \\theta _ { G } \\rVert + \\epsilon\n$$", + "text_format": "latex", + "bbox": [ + 428, + 397, + 573, + 416 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "The same analysis applies to the discriminator. The similar intuition is that it takes the discriminator additional effort to compensate the exploitation from the optimised $z ^ { \\prime }$ . We then obtain ", + "bbox": [ + 173, + 422, + 825, + 452 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/28bbbaec800be633c323dbece41044abf5da91701bf2a0f3981a0c739ef49503.jpg", + "text": "$$\n\\left( \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { D } } \\right) ^ { T } \\Delta \\theta _ { D } = \\left( \\frac { \\partial f ( z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial z } \\right) ^ { T } \\Delta z + \\left( \\frac { \\partial f ( z + \\Delta z ; \\theta _ { D } , \\theta _ { G } ) } { \\partial \\theta _ { D } } \\right) ^ { T } \\delta \\theta _ { D } + \\epsilon\n$$", + "text_format": "latex", + "bbox": [ + 183, + 457, + 794, + 496 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "However, since the adversarial loss $L _ { D } = - L _ { G }$ , we have $\\begin{array} { r } { \\Delta \\theta _ { D } = - \\alpha \\frac { \\partial f ( \\boldsymbol { z } ; \\boldsymbol { \\theta } _ { D } , \\boldsymbol { \\theta } _ { G } ) } { \\partial \\boldsymbol { \\theta } _ { D } } } \\end{array}$ and $\\delta \\theta _ { D } =$ $\\begin{array} { r } { - \\alpha \\frac { \\partial f ( \\boldsymbol { z } ; \\boldsymbol { \\theta } _ { D } , \\boldsymbol { \\theta } _ { G } ) } { \\partial \\boldsymbol { \\theta } _ { D } } } \\end{array}$ taking the opposite signs of eq.33. For sufficiently small $\\Delta z$ , $\\Delta \\theta _ { G }$ and $\\delta \\theta _ { G }$ , $\\epsilon$ is close to zero, so $\\lVert \\Delta \\theta _ { D } \\rVert < \\lVert \\delta \\theta _ { D } \\rVert$ under our assumptions of small $\\Delta z , \\Delta \\theta _ { G }$ and $\\delta \\theta _ { G }$ . ", + "bbox": [ + 174, + 503, + 826, + 558 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "mportantly, the bigger the product . Moreover, bigger step increases $\\frac { \\partial f ( z ) } { \\partial z } \\Delta z$ is, the more robust the id gap between updating qual and is to the error from, further facilitating $\\epsilon$ $\\mathbf { D }$ $\\mathbf { G }$ convergence according to Heusel et al. (2017). Overall, our analysis suggests: ", + "bbox": [ + 174, + 563, + 826, + 609 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "1. More than one gradient descent step may not be helpful, since $\\Delta z$ from multiple GD steps may deviate from the direction of $\\frac { \\partial f ( z ) } { \\partial z }$ . \n2. Large step of $\\Delta z$ is more helpful in facilitating convergence by widening the gap between $\\mathbf { D }$ and $\\mathbf { G }$ updates (Heusel et al., 2017). \n3. However, the step of $\\Delta z$ cannot be too large. In addition to the linear approximation we used throughout our analysis, the approximate SGA breaks down when eq.21 is strongly violated when “overshoot” brings the gradients at $\\frac { \\partial f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } }$ to the opposite sign of $\\frac { \\partial f ( z ) } { \\partial z }$ . ", + "bbox": [ + 210, + 619, + 825, + 738 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "C POISSON LIKELIHOOD FROM HINGE LOSS ", + "text_level": 1, + "bbox": [ + 173, + 756, + 558, + 773 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Here we provide a probabilistic interpretation of the hinge loss for the generator, which leads naturally to the scenario of a family of discriminators. Although this interpretation is not necessary for our current algorithm, it may provides useful guidance for incorporating multiple discriminators. ", + "bbox": [ + 173, + 789, + 825, + 832 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "We introduce the label $t = 1$ for real data and $t = 0$ fake samples. This section shows that the generator hinge loss ", + "bbox": [ + 173, + 837, + 825, + 866 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/5e64840cde5a5c641e9934aeafb0830a37f1c284d9c281b4f67191fac2af05dc.jpg", + "text": "$$\nL _ { G } = - D \\left( G ( z ) \\right)\n$$", + "text_format": "latex", + "bbox": [ + 437, + 866, + 562, + 882 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "can be interpreted as a negative log-likelihood function: ", + "bbox": [ + 173, + 886, + 540, + 901 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/755e51838e95d4086e4f2d4e3f6d5584b88bafa3dac29a07a08babae1248718b.jpg", + "text": "$$\nL _ { G } = - \\ln p ( t = 1 ; D , G ( z ) )\n$$", + "text_format": "latex", + "bbox": [ + 400, + 909, + 598, + 925 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Here $p ( t = 1 ; z , D , G )$ is the probability that the generated image $G ( z )$ can fool the discriminator $D$ . ", + "bbox": [ + 171, + 102, + 825, + 132 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "The original GAN’s discriminator can be interpreted as outputting a Bernoulli distribution $p ( t ; \\beta _ { G } ) \\mathbf { \\bar { \\alpha } } = \\mathbf { \\alpha } \\beta _ { G } ^ { t } \\cdot ( 1 - \\beta _ { G } ) ^ { 1 - t }$ . In this case, if we parameterise $\\beta _ { G } \\ \\bar { = } \\ D \\left( G ( z ) \\right)$ , the generator loss is the negative log-likelihood ", + "bbox": [ + 173, + 138, + 826, + 181 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/ebe3d36a3729558f24b9cb6f44eeb628b0b67246301244d5f6ca76a9dfff6414.jpg", + "text": "$$\n- \\ln P \\big ( t = 1 ; D , G ( z ) \\big ) = - \\ln p ( t = 1 ; \\beta _ { G } ) = - \\ln \\beta _ { G } = - \\ln D \\left( G ( z ) \\right)\n$$", + "text_format": "latex", + "bbox": [ + 253, + 186, + 745, + 205 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Bernoulli, however, is not the only valid choice as the discriminator’s output distribution. Instead of sampling “1” or $ { { } ^ { 6 } } { 0 ^ { 9 } }$ , we assume that there are many identical discriminators that can independently vote to reject an input sample as fake. The number of votes $k$ in a given interval can be described by a Poisson distribution with parameter $\\lambda$ with the following PMF: ", + "bbox": [ + 173, + 218, + 825, + 275 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/573cd2159ad10fe7c4e31950d16db1c118bbf937fdb1deeca3c568b63402b823.jpg", + "text": "$$\np ( k ; \\lambda ) = \\frac { \\lambda ^ { k } e ^ { - \\lambda } } { k ! }\n$$", + "text_format": "latex", + "bbox": [ + 437, + 280, + 558, + 314 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "The probability that a generated image can fool all the discriminators is the probability of $G ( z )$ receiving no vote for rejection ", + "bbox": [ + 173, + 327, + 825, + 354 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/a64e4aa0d35d4a74b8b0ce7c8219d18a532639a209e45b708027d63b0f26d3d9.jpg", + "text": "$$\np ( k = 0 ; \\lambda ) = e ^ { - \\lambda }\n$$", + "text_format": "latex", + "bbox": [ + 434, + 353, + 562, + 372 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Therefore, we have the following negative log-likelihood as the generator loss if we parameterise $\\lambda = - D \\left( G ( z ) \\right)$ : ", + "bbox": [ + 173, + 375, + 826, + 404 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/3d3841bcb9452892eb0bbfa152b70e2643e23e6889ec6905dd315b3e7dd4720c.jpg", + "text": "$$\n- \\ln p \\big ( k = 0 ; D , G ( z ) \\big ) = - \\ln p ( k = 0 ; \\lambda ) = - D \\left( G ( z ) \\right)\n$$", + "text_format": "latex", + "bbox": [ + 303, + 410, + 694, + 429 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "This interpretation has a caveat that when $D \\left( G ( z ) \\right) > 0$ the Poisson distribution is not well defined. However, in general the discriminator’s hinge loss ", + "bbox": [ + 173, + 434, + 823, + 464 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/f506e926681df9be3127dca9453aa7f63c40e5f7a47543976a043e5dd36fcbad.jpg", + "text": "$$\n{ \\cal L } _ { D } = - \\operatorname * { m i n } \\left( 0 , - 1 + D ( x ) \\right) - \\operatorname * { m i n } \\left( 0 , - 1 - D ( G ( z ) ) \\right)\n$$", + "text_format": "latex", + "bbox": [ + 307, + 468, + 691, + 488 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "pushes $D \\left( G ( z ) \\right) < 0$ via training. ", + "bbox": [ + 173, + 494, + 400, + 511 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "D DETAILS IN COMPUTING DISTANCES IN FIGURE 5 A ", + "text_level": 1, + "bbox": [ + 174, + 529, + 642, + 546 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "For a temporal sequence $x _ { 1 } , x _ { 2 } , \\ldots , x _ { T }$ (changes of $z$ or $f ( z )$ at each training step in this paper), to normalise its variance while accounting for the non-stationarity, we process it as follows. We first compute the moving average and standard deviation over a window of size $N$ : ", + "bbox": [ + 173, + 560, + 825, + 603 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/b0054f0e51f8d020f82fc7d0c8c600504cd099f7774e67ecc59e938693dca699.jpg", + "text": "$$\n\\begin{array} { l } { \\displaystyle \\mu _ { t } = \\frac { 1 } { N } \\sum _ { u = t } ^ { t + N - 1 } x _ { u } } \\\\ { \\displaystyle \\sigma _ { t } = \\sqrt { \\frac { 1 } { N - 1 } \\sum _ { u = t } ^ { t + N - 1 } ( x _ { u } - \\mu _ { u } ) ^ { 2 } } } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 383, + 609, + 614, + 705 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Then normalise the sequence as: ", + "bbox": [ + 174, + 709, + 388, + 724 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/e90cbb7d2f2f1acf6e5335ac6e4d56ab6f2452c87406e52e43ed256b920d562c.jpg", + "text": "$$\n\\bar { x } _ { t } = \\frac { x _ { t } } { \\sigma _ { t } }\n$$", + "text_format": "latex", + "bbox": [ + 468, + 722, + 529, + 751 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "The result in Figure ${ \\bf 5 a }$ is robust to the choice of window size. Our experiments with $N$ from 10 to 50 yielded visually similar plots. ", + "bbox": [ + 173, + 752, + 825, + 781 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "E EXPERIMENTS WITH DCGAN AND CIFAR", + "text_level": 1, + "bbox": [ + 173, + 800, + 565, + 818 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "To test if latent optimisation works with models at more moderate scales, we applied it on SN-GANs (Miyato et al., 2018). Although our experiments on this model are less thorough than in the main paper with BigGAN-deep, we hope to provide basic guidelines for researchers interested in applying latent optimisation on smaller models. ", + "bbox": [ + 174, + 832, + 825, + 888 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "The experiments follows the same basic setup and hyper-parameter settings as the CS-GAN in Wu et al. (2019). There is no class conditioning in this model. For NGD, we found a smaller damping factor $\\beta = 0 . 1$ , a $\\| z \\|$ regulariser weight of 3.0 (the same as in $\\mathbf { W } \\mathbf { u }$ et al. 2019), combined with optimising $7 0 \\%$ of the latent source (instead of $5 0 \\%$ for BigGAN-deep) worked best for SN-GANs. ", + "bbox": [ + 173, + 895, + 823, + 924 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 103, + 823, + 132 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "In addition, we found running extra latent optimisation steps benefited evaluation, so we use ten steps of latent optimisation in evaluation for results in this section, although the models were still trained with a single optimisation step. We reckon that smaller models might not be “over-parametrised” enough to fully amortise the computation from optimising $z$ , which can then further exploit the architecture in evaluation time. On the other hand, the overhead from running multiple iterations of latent optimisation is relatively small at this scale. We aim to further investigate this difference in future studies. ", + "bbox": [ + 174, + 138, + 825, + 236 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Table 2 shows the FID and IS alongside SN-GAN and CS-CAN which used the same architecture. Here we observe similarly significant improvement over the baseline SN-GAN model, with an improvement of $1 6 . 8 \\%$ in IS and $3 9 . 6 \\%$ in FID. Figure 9 shows random samples from these two models. Overall, samples from LOGAN (NGD) have higher contrasts and sharper contours. ", + "bbox": [ + 174, + 242, + 825, + 300 + ], + "page_idx": 15 + }, + { + "type": "table", + "img_path": "images/8252bfa40a1cf81e7dfcd6a4941fb2e9cf65565f39901908143bf6a503a07345.jpg", + "table_caption": [ + "Table 2: Comparison of Scores. The first and second columns are reproduced from Miyato et al. (2018) and Wu et al. (2019) respectively. We report the Inception Score (IS, higher is better, Salimans et al. 2016) and Frechet Inception Distance (FID, lower is better, Heusel et al. 2017). ´ " + ], + "table_footnote": [], + "table_body": "
SN-GANCS-GANLOGAN (NGD)
FID29.323.1 ± 0.517.7 ± 0.4
IS7.42 ± 0.087.80 ± 0.058.67 ± 0.05
", + "bbox": [ + 313, + 371, + 681, + 416 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/08d18f774fc587387bb21732661c7ffc3db922b57aa6143398a3beb197685e05.jpg", + "image_caption": [ + "Figure 6: Samples from BigGAN-deep (a) and LOGAN (b) with the similarly high inception scores. Samples from the two panels were draw from truncations correspond to points C, D in figure $^ { 3 \\mathrm { ~ b ~ } }$ respectively. (FID/IS: (a) 27.97/259.4, (b) 8.19/259.9) " + ], + "image_footnote": [], + "bbox": [ + 196, + 106, + 799, + 886 + ], + "page_idx": 16 + }, + { + "type": "image", + "img_path": "images/85eb8fa1823f783151421751466d469565435d09556bb7dbba3499f3ec9b9f32.jpg", + "image_caption": [ + "Figure 7: Samples from BigGAN-deep (a) and LOGAN (b) with the similarly low FID. Samples from the two panels were draw from truncations correspond to points A, B in figure $^ { 3 } \\mathbf { b }$ respectively. (FID/IS: (a) 5.04/126.8, (b) 5.09/217.0) " + ], + "image_footnote": [], + "bbox": [ + 184, + 111, + 813, + 857 + ], + "page_idx": 17 + }, + { + "type": "image", + "img_path": "images/a84700ae275e2a00511145cb295e953cda39609b11d83381e9b2f310aeed347e.jpg", + "image_caption": [ + "Figure 8: Truncation curves with additional baselines. In addition to the truncation curves reported in Figure $^ { 3 \\mathrm { ~ b ~ } }$ , here we also include the Spectral-Normalised GAN (Miyato et al., 2018), SelfAttention GAN (Zhang et al., 2019), original BigGAN and BigGAN-deep as presented in Brock et al. (2018). " + ], + "image_footnote": [], + "bbox": [ + 238, + 121, + 758, + 515 + ], + "page_idx": 18 + }, + { + "type": "image", + "img_path": "images/da1f330a00f9fc880d248896003a11028638743649f1581001989eb4a8c5c081.jpg", + "image_caption": [ + "Figure 9: (a) Samples from SN-GAN. (b) Samples from LOGAN. 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However, despite", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 433, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 506, + 448 + ], + "score": 1.0, + "content": "growing insights into the dynamics of GAN training, most recent advances in large-scale image", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 444, + 506, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 506, + 459 + ], + "score": 1.0, + "content": "generation come from architectural improvements (Radford et al., 2015; Zhang et al., 2019), or reg-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 456, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 106, + 456, + 505, + 468 + ], + "score": 1.0, + "content": "ularisation focusing on particular parts of the model (Miyato et al., 2018; Miyato & Koyama, 2018).", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "score": 1.0, + "content": "Inspired by the compressed sensing GAN (CS-GAN; Wu et al., 2019), we further exploit the ben-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 477, + 505, + 490 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 505, + 490 + ], + "score": 1.0, + "content": "efit of latent optimisation in adversarial games using natural gradient descent to optimise the latent", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 488, + 505, + 501 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 140, + 501 + ], + "score": 1.0, + "content": "variable", + "type": "text" + }, + { + "bbox": [ + 141, + 490, + 147, + 498 + ], + "score": 0.73, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 148, + 488, + 505, + 501 + ], + "score": 1.0, + "content": "at each step of training, presenting a scalable and easy to implement approach to improve", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 499, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 106, + 499, + 505, + 511 + ], + "score": 1.0, + "content": "the dynamical interaction between the discriminator and the generator. For clarity, we unify these", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 511, + 306, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 306, + 523 + ], + "score": 1.0, + "content": "approaches as latent optimised GANs (LOGAN).", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 23.5 + }, + { + "type": "text", + "bbox": [ + 108, + 527, + 237, + 538 + ], + "lines": [ + { + "bbox": [ + 106, + 527, + 238, + 539 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 238, + 539 + ], + "score": 1.0, + "content": "To summarise our contributions:", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 130, + 547, + 505, + 645 + ], + "lines": [ + { + "bbox": [ + 129, + 548, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 129, + 548, + 505, + 561 + ], + "score": 1.0, + "content": "1. 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BigGAN-DeepbaselineLOGAN (GD)LOGAN (NGD)
FID5.7 ± 0.34.92±0.054.86±0.093.36± 0.14
IS124.5 ± 2.0126.6 ± 1.3127.7 ± 3.5148.2 ±3.1
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BigGAN-DeepbaselineLOGAN (GD)LOGAN (NGD)
FID5.7 ± 0.34.92±0.054.86±0.093.36± 0.14
IS124.5 ± 2.0126.6 ± 1.3127.7 ± 3.5148.2 ±3.1
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Our experiments with BigGAN-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 239, + 505, + 252 + ], + "spans": [ + { + "bbox": [ + 105, + 239, + 505, + 252 + ], + "score": 1.0, + "content": "deep uses the hinge loss (Lim & Ye, 2017; Tran et al., 2017), which is identical to this form in its", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 249, + 506, + 264 + ], + "spans": [ + { + "bbox": [ + 104, + 249, + 506, + 264 + ], + "score": 1.0, + "content": "linear regime. Our analysis can be generalised to other losses as in previous theoretical work (e.g.,", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 261, + 506, + 274 + ], + "spans": [ + { + "bbox": [ + 106, + 261, + 333, + 274 + ], + "score": 1.0, + "content": "Arora et al. 2017). 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A recent milestone is BigGAN", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 311, + 505, + 324 + ], + "spans": [ + { + "bbox": [ + 106, + 311, + 505, + 324 + ], + "score": 1.0, + "content": "(and BigGAN-deep, Brock et al. 2018), which pushed the boundary of high fidelity image generation", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 322, + 505, + 335 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 505, + 335 + ], + "score": 1.0, + "content": "by scaling up GANs to an unprecedented level. 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In Balduzzi et al. (2018), vector", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 499, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 499, + 505, + 513 + ], + "score": 1.0, + "content": "fields of this form are referred to as the simultaneous gradient. 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Latent", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 600, + 506, + 612 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 506, + 612 + ], + "score": 1.0, + "content": "optimization has been shown to improve the stability of training as well as the final performance for", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 609, + 505, + 623 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 505, + 623 + ], + "score": 1.0, + "content": "medium-sized models such as DCGANs and Spectral Normalised GANs (Radford et al., 2015; Miy-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 622, + 505, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 358, + 634 + ], + "score": 1.0, + "content": "ato et al., 2018). Latent optimisation exploits knowledge from", + "type": "text" + }, + { + "bbox": [ + 358, + 622, + 368, + 631 + ], + "score": 0.81, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 368, + 622, + 448, + 634 + ], + "score": 1.0, + "content": "to guide updates of", + "type": "text" + }, + { + "bbox": [ + 448, + 623, + 455, + 631 + ], + "score": 0.76, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 455, + 622, + 505, + 634 + ], + "score": 1.0, + "content": ". 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(b) Truncation curves illustrate the FID/IS trade-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 342, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 356, + 354 + ], + "score": 1.0, + "content": "off for each model by altering the range of the noise source", + "type": "text" + }, + { + "bbox": [ + 356, + 342, + 375, + 354 + ], + "score": 0.91, + "content": "p ( z )", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 342, + 505, + 354 + ], + "score": 1.0, + "content": ". GD: gradient descent. NGD:", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 353, + 473, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 473, + 366 + ], + "score": 1.0, + "content": "natural gradient descent. Points A, B, C, D correspond to samples shown in Figure 1 and 2.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 6 + } + ], + "index": 3.5 + }, + { + "type": "table", + "bbox": [ + 109, + 391, + 502, + 561 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 377, + 386, + 389 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 377, + 387, + 391 + ], + "spans": [ + { + "bbox": [ + 106, + 377, + 387, + 391 + ], + "score": 1.0, + "content": "Algorithm 1 Latent Optimised GANs with Automatic Differentiation", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "table_body", + "bbox": [ + 109, + 391, + 502, + 561 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 391, + 502, + 561 + ], + "spans": [ + { + "bbox": [ + 109, + 391, + 502, + 561 + ], + "score": 0.752, + "html": "
Input: data distribution p(x),latent distribution p(z),D(:; 0D), G(-; 0g),learning rate α, batch size N repeat
Initialise discriminator and generator parameters 0D,0G fori=1 to Ndo
Sample z ~ p(z),x~p(x)
Compute the gradient D(G(z)) and use it to obtain △z from eq. 4 (GD) or eq. 12 (NGD) dz
Optimise the latent z' ← [+ △z],[:] indicates clipping the value between -1 and 1
= -D(G(z))
D(G(z'))-D(x) end for
Compute batch losses LG =N∑i=11 JN (i) and LD=∑=1 N L(i) LD
aLD aLG Update 0D and 0G with the gradients
0D， G
until reaches the maximum training steps
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(2018); Gemp & Mahadevan (2018); Letcher et al.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 630, + 506, + 643 + ], + "spans": [ + { + "bbox": [ + 105, + 630, + 506, + 643 + ], + "score": 1.0, + "content": "(2019). The appendix provides a complementary analysis that relates LOGAN to unrolled GANs", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 641, + 446, + 653 + ], + "spans": [ + { + "bbox": [ + 106, + 641, + 446, + 653 + ], + "score": 1.0, + "content": "(Metz et al., 2016) and stochastic approximation (Heusel et al., 2017; Borkar, 1997).", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16.5 + }, + { + "type": "title", + "bbox": [ + 106, + 666, + 350, + 678 + ], + "lines": [ + { + "bbox": [ + 105, + 665, + 350, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 350, + 680 + ], + "score": 1.0, + "content": "3.1 THE SYMPLECTIC GRADIENT ADJUSTMENT (SGA)", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 687, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "An important problem with gradient-based optimization in GANs is that the vector-field generated", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "by the losses of the discriminator and generator is not a gradient vector field. It follows that gradient", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "descent is not guaranteed to find a local optimum and can cycle, which can slow down convergence", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "score": 1.0, + "content": "or lead to phenomena like mode collapse and mode hopping. Balduzzi et al. (2018); Gemp &", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 114, + 82, + 493, + 278 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 114, + 82, + 493, + 278 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 114, + 82, + 493, + 278 + ], + "spans": [ + { + "bbox": [ + 114, + 82, + 493, + 278 + ], + "score": 0.965, + "type": "image", + "image_path": "c24ba41202d98dd0cfb864fbd092fb035f3fe4c84763666ad586e37a8cf9c30d.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 114, + 82, + 493, + 147.33333333333331 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 114, + 147.33333333333331, + 493, + 212.66666666666663 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 114, + 212.66666666666663, + 493, + 277.99999999999994 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 287, + 506, + 365 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 286, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 435, + 300 + ], + "score": 1.0, + "content": "Figure 3: (a) Schematic of LOGAN. 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(b) Truncation curves illustrate the FID/IS trade-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 342, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 356, + 354 + ], + "score": 1.0, + "content": "off for each model by altering the range of the noise source", + "type": "text" + }, + { + "bbox": [ + 356, + 342, + 375, + 354 + ], + "score": 0.91, + "content": "p ( z )", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 342, + 505, + 354 + ], + "score": 1.0, + "content": ". GD: gradient descent. NGD:", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 353, + 473, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 473, + 366 + ], + "score": 1.0, + "content": "natural gradient descent. Points A, B, C, D correspond to samples shown in Figure 1 and 2.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 6 + } + ], + "index": 3.5 + }, + { + "type": "table", + "bbox": [ + 109, + 391, + 502, + 561 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 377, + 386, + 389 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 377, + 387, + 391 + ], + "spans": [ + { + "bbox": [ + 106, + 377, + 387, + 391 + ], + "score": 1.0, + "content": "Algorithm 1 Latent Optimised GANs with Automatic Differentiation", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "table_body", + "bbox": [ + 109, + 391, + 502, + 561 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 391, + 502, + 561 + ], + "spans": [ + { + "bbox": [ + 109, + 391, + 502, + 561 + ], + "score": 0.752, + "html": "
Input: data distribution p(x),latent distribution p(z),D(:; 0D), G(-; 0g),learning rate α, batch size N repeat
Initialise discriminator and generator parameters 0D,0G fori=1 to Ndo
Sample z ~ p(z),x~p(x)
Compute the gradient D(G(z)) and use it to obtain △z from eq. 4 (GD) or eq. 12 (NGD) dz
Optimise the latent z' ← [+ △z],[:] indicates clipping the value between -1 and 1
= -D(G(z))
D(G(z'))-D(x) end for
Compute batch losses LG =N∑i=11 JN (i) and LD=∑=1 N L(i) LD
aLD aLG Update 0D and 0G with the gradients
0D， G
until reaches the maximum training steps
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SGA uses the adjusted", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 115, + 143, + 127 + ], + "spans": [ + { + "bbox": [ + 104, + 115, + 143, + 127 + ], + "score": 1.0, + "content": "gradient", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "interline_equation", + "bbox": [ + 205, + 125, + 407, + 140 + ], + "lines": [ + { + "bbox": [ + 205, + 125, + 407, + 140 + ], + "spans": [ + { + "bbox": [ + 205, + 125, + 407, + 140 + ], + "score": 0.8, + "content": "g ^ { * } = g + \\lambda A ^ { T } g \\quad { \\mathrm { w h e r e ~ } } \\lambda { \\mathrm { ~ i s ~ a ~ p o s i t i v e ~ c o n s t a n t } }", + "type": "interline_equation", + "image_path": "2f712f91570b8cabf50bafb2c9192f40a2b4dd9910cc127fcc455f6eab5db2b9.jpg" + } + ] + } + ], + "index": 4, + "virtual_lines": [ + { + "bbox": [ + 205, + 125, + 407, + 140 + ], + "spans": [], + "index": 4 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 142, + 504, + 165 + ], + "lines": [ + { + "bbox": [ + 105, + 140, + 506, + 155 + ], + "spans": [ + { + "bbox": [ + 105, + 140, + 124, + 155 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 124, + 141, + 199, + 155 + ], + "score": 0.93, + "content": "\\begin{array} { r } { A = \\frac 1 2 ( H - H ^ { T } ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 200, + 140, + 506, + 155 + ], + "score": 1.0, + "content": "is the anti-symmetric component of the Hessian. 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All other hyper-parameters, including learning rates and a large batch size of 2048, remain", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "the same as in BigGAN-deep; we did not optimise these hyper-parameters. We call this model", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 177, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 177, + 117 + ], + "score": 1.0, + "content": "LOGAN (NGD).", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "title", + "bbox": [ + 107, + 135, + 200, + 146 + ], + "lines": [ + { + "bbox": [ + 105, + 133, + 201, + 148 + ], + "spans": [ + { + "bbox": [ + 105, + 133, + 201, + 148 + ], + "score": 1.0, + "content": "5.2 BASIC RESULTS", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 107, + 157, + 505, + 213 + ], + "lines": [ + { + "bbox": [ + 106, + 158, + 505, + 170 + ], + "spans": [ + { + "bbox": [ + 106, + 158, + 505, + 170 + ], + "score": 1.0, + "content": "Employing the same architecture and number of parameters as the BigGAN-deep baseline, LOGAN", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 167, + 505, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 167, + 505, + 182 + ], + "score": 1.0, + "content": "(NGD) achieved better FID and IS (Table 1). As observed by Brock et al. (2018), BigGAN training", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 180, + 505, + 193 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 505, + 193 + ], + "score": 1.0, + "content": "always eventually collapsed. Training with LOGAN also collapsed, perhaps due to higher-order", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 190, + 504, + 204 + ], + "spans": [ + { + "bbox": [ + 105, + 190, + 482, + 204 + ], + "score": 1.0, + "content": "dynamics beyond the scope we have analysed, but took significantly longer (600k steps versus", + "type": "text" + }, + { + "bbox": [ + 482, + 191, + 504, + 201 + ], + "score": 0.33, + "content": "3 0 0 \\mathrm { k }", + "type": "inline_equation" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 201, + 214, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 201, + 214, + 215 + ], + "score": 1.0, + "content": "steps with BigGAN-deep).", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 106, + 218, + 505, + 318 + ], + "lines": [ + { + "bbox": [ + 105, + 218, + 506, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 231, + 232 + ], + "score": 1.0, + "content": "During training, LOGAN was", + "type": "text" + }, + { + "bbox": [ + 231, + 219, + 256, + 229 + ], + "score": 0.3, + "content": "2 - 3", + "type": "inline_equation" + }, + { + "bbox": [ + 256, + 218, + 506, + 232 + ], + "score": 1.0, + "content": "times slower per step compared with BigGAN-deep because", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 229, + 505, + 242 + ], + "spans": [ + { + "bbox": [ + 105, + 229, + 406, + 242 + ], + "score": 1.0, + "content": "of the additional forward and backward pass. We found that optimising", + "type": "text" + }, + { + "bbox": [ + 407, + 232, + 414, + 240 + ], + "score": 0.76, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 414, + 229, + 505, + 242 + ], + "score": 1.0, + "content": "during evaluation did", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 241, + 505, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 403, + 253 + ], + "score": 1.0, + "content": "not improve sample scores (even up to 10 steps), so we do not optimise", + "type": "text" + }, + { + "bbox": [ + 403, + 243, + 410, + 250 + ], + "score": 0.74, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 241, + 505, + 253 + ], + "score": 1.0, + "content": "for evaluation. There-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 251, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 251, + 505, + 264 + ], + "score": 1.0, + "content": "fore, LOGAN has the same evaluation cost as original BigGAN-deep. To help understand this", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 261, + 506, + 277 + ], + "spans": [ + { + "bbox": [ + 104, + 261, + 254, + 277 + ], + "score": 1.0, + "content": "behaviour, we plot the change from", + "type": "text" + }, + { + "bbox": [ + 254, + 263, + 269, + 273 + ], + "score": 0.85, + "content": "\\Delta z", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 261, + 506, + 277 + ], + "score": 1.0, + "content": "during training in Figure 5 a. Although the movement in", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 272, + 506, + 286 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 174, + 286 + ], + "score": 1.0, + "content": "Euclidean space", + "type": "text" + }, + { + "bbox": [ + 174, + 273, + 198, + 285 + ], + "score": 0.9, + "content": "| | \\Delta z | |", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 272, + 390, + 286 + ], + "score": 1.0, + "content": "grew until training collapsed, the movement in", + "type": "text" + }, + { + "bbox": [ + 390, + 274, + 400, + 284 + ], + "score": 0.75, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 272, + 506, + 286 + ], + "score": 1.0, + "content": "’s output space, measured", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 284, + 506, + 297 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 118, + 297 + ], + "score": 1.0, + "content": "as", + "type": "text" + }, + { + "bbox": [ + 118, + 284, + 204, + 297 + ], + "score": 0.92, + "content": "\\| f ( z + \\Delta z ) - f ( z ) \\|", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 284, + 353, + 297 + ], + "score": 1.0, + "content": ", remained unchanged (see Appendix", + "type": "text" + }, + { + "bbox": [ + 354, + 285, + 363, + 295 + ], + "score": 0.29, + "content": "\\mathrm { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 284, + 506, + 297 + ], + "score": 1.0, + "content": "for details). As shown in our anal-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 295, + 506, + 308 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 174, + 308 + ], + "score": 1.0, + "content": "ysis, optimising", + "type": "text" + }, + { + "bbox": [ + 174, + 298, + 181, + 305 + ], + "score": 0.7, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 295, + 506, + 308 + ], + "score": 1.0, + "content": "improves the training dynamics, so LOGANs work well after training without", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 306, + 225, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 225, + 320 + ], + "score": 1.0, + "content": "requiring latent optimisation.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 13 + }, + { + "type": "title", + "bbox": [ + 108, + 336, + 216, + 348 + ], + "lines": [ + { + "bbox": [ + 105, + 335, + 218, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 218, + 350 + ], + "score": 1.0, + "content": "5.3 ABLATION STUDIES", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 359, + 505, + 415 + ], + "lines": [ + { + "bbox": [ + 106, + 360, + 505, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 505, + 372 + ], + "score": 1.0, + "content": "We verify our theoretical analysis in section 3 by examining key components of Algorithm 1 via", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 370, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 405, + 384 + ], + "score": 1.0, + "content": "ablation studies. First, we experimented with using basic GD to optimising", + "type": "text" + }, + { + "bbox": [ + 406, + 373, + 412, + 381 + ], + "score": 0.64, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 370, + 505, + 384 + ], + "score": 1.0, + "content": ", as in Wu et al. (2019),", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 382, + 505, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 342, + 394 + ], + "score": 1.0, + "content": "and call this model LOGAN (GD). A smaller step size of", + "type": "text" + }, + { + "bbox": [ + 342, + 382, + 392, + 392 + ], + "score": 0.88, + "content": "\\alpha = 0 . 0 0 0 1", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 382, + 505, + 394 + ], + "score": 1.0, + "content": "was required; larger values", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 393, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 393, + 505, + 405 + ], + "score": 1.0, + "content": "were unstable and led to premature collapse of training. As shown in Table 1, the scores from", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 404, + 440, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 404, + 440, + 416 + ], + "score": 1.0, + "content": "LOGAN (GD) were worse than LOGAN (NGD) and similar to the baseline model.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 420, + 505, + 520 + ], + "lines": [ + { + "bbox": [ + 105, + 417, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 378, + 447 + ], + "score": 1.0, + "content": "We then evaluate the effects of removing those terms depending on the ordinary gradient (eq. 3). Since these terms were computed", + "type": "text" + }, + { + "bbox": [ + 379, + 420, + 401, + 435 + ], + "score": 0.92, + "content": "\\frac { \\partial f ( z ) } { \\partial z }", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 417, + 505, + 447 + ], + "score": 1.0, + "content": "in eq. 8, which are not inback-propagating through", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 445, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 445, + 505, + 456 + ], + "score": 1.0, + "content": "the latent optimisation procedure, we removed them by selectively blocking back-propagation", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 455, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 106, + 455, + 460, + 468 + ], + "score": 1.0, + "content": "with “stop gradient” operations (e.g., in TensorFlow Abadi et al. 2016). Figure", + "type": "text" + }, + { + "bbox": [ + 460, + 456, + 476, + 466 + ], + "score": 0.69, + "content": "{ \\bf 5 \\ B }", + "type": "inline_equation" + }, + { + "bbox": [ + 477, + 455, + 506, + 468 + ], + "score": 1.0, + "content": "shows", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 466, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 394, + 487 + ], + "score": 1.0, + "content": "the change of FIDs for the three models corresponding to removing", + "type": "text" + }, + { + "bbox": [ + 394, + 466, + 459, + 489 + ], + "score": 0.93, + "content": "\\left( \\frac { \\partial \\Delta z } { \\partial \\theta _ { G } } \\right) ^ { T } \\ \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } }", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 466, + 505, + 487 + ], + "score": 1.0, + "content": ", removing", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 107, + 487, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 107, + 487, + 171, + 510 + ], + "score": 0.92, + "content": "\\begin{array} { r } { \\left( \\frac { \\partial \\Delta z } { \\partial \\theta _ { D } } \\right) ^ { T } \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 172, + 487, + 505, + 510 + ], + "score": 1.0, + "content": "and removing both terms. As predicted by our analysis (section 3), both terms help", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 507, + 361, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 361, + 520 + ], + "score": 1.0, + "content": "stabilise training; training diverged early for all three ablations.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26.5 + }, + { + "type": "title", + "bbox": [ + 108, + 538, + 252, + 549 + ], + "lines": [ + { + "bbox": [ + 106, + 538, + 254, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 254, + 551 + ], + "score": 1.0, + "content": "5.4 TRUNCATION AND SAMPLES", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 561, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "score": 1.0, + "content": "Truncation is a technique introduced by Brock et al. (2018) to illustrate the trade-off between the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 572, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 350, + 584 + ], + "score": 1.0, + "content": "FID and IS in a trained model. For a model trained with", + "type": "text" + }, + { + "bbox": [ + 351, + 572, + 393, + 583 + ], + "score": 0.91, + "content": "z \\sim p ( z )", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 572, + 505, + 584 + ], + "score": 1.0, + "content": "from a source distribution", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 104, + 582, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 104, + 582, + 355, + 596 + ], + "score": 1.0, + "content": "symmetric around 0, such as the standard normal distribution", + "type": "text" + }, + { + "bbox": [ + 355, + 583, + 388, + 595 + ], + "score": 0.9, + "content": "\\mathcal { N } ( 0 , 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 582, + 506, + 596 + ], + "score": 1.0, + "content": "and the uniform distribution", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 594, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 144, + 606 + ], + "score": 0.91, + "content": "\\mathcal { U } ( - 1 , 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 145, + 594, + 297, + 607 + ], + "score": 1.0, + "content": ", down-scaling (truncating) the source", + "type": "text" + }, + { + "bbox": [ + 297, + 595, + 334, + 604 + ], + "score": 0.9, + "content": "\\bar { z } = s \\cdot z", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 594, + 355, + 607 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 356, + 595, + 398, + 605 + ], + "score": 0.9, + "content": "0 \\leq s \\leq 1", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 594, + 505, + 607 + ], + "score": 1.0, + "content": "gives samples with higher", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "visual quality but reduced diversity. This observation is quantified as higher IS and lower FID when", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 617, + 300, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 300, + 628 + ], + "score": 1.0, + "content": "evaluating samples from truncated distributions.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 33.5 + }, + { + "type": "text", + "bbox": [ + 106, + 632, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 633, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 135, + 645 + ], + "score": 1.0, + "content": "Figure", + "type": "text" + }, + { + "bbox": [ + 136, + 633, + 152, + 643 + ], + "score": 0.6, + "content": "^ { 3 \\mathrm { ~ b ~ } }", + "type": "inline_equation" + }, + { + "bbox": [ + 152, + 633, + 505, + 645 + ], + "score": 1.0, + "content": "plots the truncation curves for the baseline BigGAN-deep model, LOGAN (GD) and", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 644, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 354, + 657 + ], + "score": 1.0, + "content": "LOGAN (NGD), obtained by varying the truncation (value of", + "type": "text" + }, + { + "bbox": [ + 355, + 646, + 361, + 654 + ], + "score": 0.56, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 644, + 506, + 657 + ], + "score": 1.0, + "content": ") from 1.0 (no truncation, upper-left", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "ends of the curves) to 0.02 (extreme truncation, bottom-right ends). Each curve shows the trade-off", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 665, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 506, + 678 + ], + "score": 1.0, + "content": "between FID and IS for an individual model; curves towards the upper-right corner indicate better", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 676, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 505, + 689 + ], + "score": 1.0, + "content": "overall sample quality. The relative positions of curves in Figure 3 (b) shows LOGAN (NGD) has", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "the best sample quality. Interestingly, although LOGAN (GD) and the baseline model have similar", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "score": 1.0, + "content": "scores without truncation (upper-left ends of the curves, see also Table 1), LOGAN (GD) was better", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "behaved with increasing truncation, suggesting LOGAN (GD) still converged to a better equilibrium.", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 720, + 477, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 477, + 733 + ], + "score": 1.0, + "content": "For further reference, we plot truncation curves from additional baseline models in Figure 8.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 41 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "score": 1.0, + "content": "8", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 107, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 107, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 504, + 116 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 506, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 506, + 95 + ], + "score": 1.0, + "content": "300.0. All other hyper-parameters, including learning rates and a large batch size of 2048, remain", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "the same as in BigGAN-deep; we did not optimise these hyper-parameters. We call this model", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 177, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 177, + 117 + ], + "score": 1.0, + "content": "LOGAN (NGD).", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1, + "bbox_fs": [ + 105, + 82, + 506, + 117 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 135, + 200, + 146 + ], + "lines": [ + { + "bbox": [ + 105, + 133, + 201, + 148 + ], + "spans": [ + { + "bbox": [ + 105, + 133, + 201, + 148 + ], + "score": 1.0, + "content": "5.2 BASIC RESULTS", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 107, + 157, + 505, + 213 + ], + "lines": [ + { + "bbox": [ + 106, + 158, + 505, + 170 + ], + "spans": [ + { + "bbox": [ + 106, + 158, + 505, + 170 + ], + "score": 1.0, + "content": "Employing the same architecture and number of parameters as the BigGAN-deep baseline, LOGAN", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 167, + 505, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 167, + 505, + 182 + ], + "score": 1.0, + "content": "(NGD) achieved better FID and IS (Table 1). As observed by Brock et al. (2018), BigGAN training", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 180, + 505, + 193 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 505, + 193 + ], + "score": 1.0, + "content": "always eventually collapsed. Training with LOGAN also collapsed, perhaps due to higher-order", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 190, + 504, + 204 + ], + "spans": [ + { + "bbox": [ + 105, + 190, + 482, + 204 + ], + "score": 1.0, + "content": "dynamics beyond the scope we have analysed, but took significantly longer (600k steps versus", + "type": "text" + }, + { + "bbox": [ + 482, + 191, + 504, + 201 + ], + "score": 0.33, + "content": "3 0 0 \\mathrm { k }", + "type": "inline_equation" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 201, + 214, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 201, + 214, + 215 + ], + "score": 1.0, + "content": "steps with BigGAN-deep).", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 6, + "bbox_fs": [ + 105, + 158, + 505, + 215 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 218, + 505, + 318 + ], + "lines": [ + { + "bbox": [ + 105, + 218, + 506, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 231, + 232 + ], + "score": 1.0, + "content": "During training, LOGAN was", + "type": "text" + }, + { + "bbox": [ + 231, + 219, + 256, + 229 + ], + "score": 0.3, + "content": "2 - 3", + "type": "inline_equation" + }, + { + "bbox": [ + 256, + 218, + 506, + 232 + ], + "score": 1.0, + "content": "times slower per step compared with BigGAN-deep because", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 229, + 505, + 242 + ], + "spans": [ + { + "bbox": [ + 105, + 229, + 406, + 242 + ], + "score": 1.0, + "content": "of the additional forward and backward pass. We found that optimising", + "type": "text" + }, + { + "bbox": [ + 407, + 232, + 414, + 240 + ], + "score": 0.76, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 414, + 229, + 505, + 242 + ], + "score": 1.0, + "content": "during evaluation did", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 241, + 505, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 403, + 253 + ], + "score": 1.0, + "content": "not improve sample scores (even up to 10 steps), so we do not optimise", + "type": "text" + }, + { + "bbox": [ + 403, + 243, + 410, + 250 + ], + "score": 0.74, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 241, + 505, + 253 + ], + "score": 1.0, + "content": "for evaluation. There-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 251, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 251, + 505, + 264 + ], + "score": 1.0, + "content": "fore, LOGAN has the same evaluation cost as original BigGAN-deep. To help understand this", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 261, + 506, + 277 + ], + "spans": [ + { + "bbox": [ + 104, + 261, + 254, + 277 + ], + "score": 1.0, + "content": "behaviour, we plot the change from", + "type": "text" + }, + { + "bbox": [ + 254, + 263, + 269, + 273 + ], + "score": 0.85, + "content": "\\Delta z", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 261, + 506, + 277 + ], + "score": 1.0, + "content": "during training in Figure 5 a. Although the movement in", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 272, + 506, + 286 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 174, + 286 + ], + "score": 1.0, + "content": "Euclidean space", + "type": "text" + }, + { + "bbox": [ + 174, + 273, + 198, + 285 + ], + "score": 0.9, + "content": "| | \\Delta z | |", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 272, + 390, + 286 + ], + "score": 1.0, + "content": "grew until training collapsed, the movement in", + "type": "text" + }, + { + "bbox": [ + 390, + 274, + 400, + 284 + ], + "score": 0.75, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 272, + 506, + 286 + ], + "score": 1.0, + "content": "’s output space, measured", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 284, + 506, + 297 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 118, + 297 + ], + "score": 1.0, + "content": "as", + "type": "text" + }, + { + "bbox": [ + 118, + 284, + 204, + 297 + ], + "score": 0.92, + "content": "\\| f ( z + \\Delta z ) - f ( z ) \\|", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 284, + 353, + 297 + ], + "score": 1.0, + "content": ", remained unchanged (see Appendix", + "type": "text" + }, + { + "bbox": [ + 354, + 285, + 363, + 295 + ], + "score": 0.29, + "content": "\\mathrm { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 284, + 506, + 297 + ], + "score": 1.0, + "content": "for details). As shown in our anal-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 295, + 506, + 308 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 174, + 308 + ], + "score": 1.0, + "content": "ysis, optimising", + "type": "text" + }, + { + "bbox": [ + 174, + 298, + 181, + 305 + ], + "score": 0.7, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 295, + 506, + 308 + ], + "score": 1.0, + "content": "improves the training dynamics, so LOGANs work well after training without", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 306, + 225, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 225, + 320 + ], + "score": 1.0, + "content": "requiring latent optimisation.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 13, + "bbox_fs": [ + 104, + 218, + 506, + 320 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 336, + 216, + 348 + ], + "lines": [ + { + "bbox": [ + 105, + 335, + 218, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 218, + 350 + ], + "score": 1.0, + "content": "5.3 ABLATION STUDIES", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 359, + 505, + 415 + ], + "lines": [ + { + "bbox": [ + 106, + 360, + 505, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 505, + 372 + ], + "score": 1.0, + "content": "We verify our theoretical analysis in section 3 by examining key components of Algorithm 1 via", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 370, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 405, + 384 + ], + "score": 1.0, + "content": "ablation studies. First, we experimented with using basic GD to optimising", + "type": "text" + }, + { + "bbox": [ + 406, + 373, + 412, + 381 + ], + "score": 0.64, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 370, + 505, + 384 + ], + "score": 1.0, + "content": ", as in Wu et al. (2019),", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 382, + 505, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 342, + 394 + ], + "score": 1.0, + "content": "and call this model LOGAN (GD). A smaller step size of", + "type": "text" + }, + { + "bbox": [ + 342, + 382, + 392, + 392 + ], + "score": 0.88, + "content": "\\alpha = 0 . 0 0 0 1", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 382, + 505, + 394 + ], + "score": 1.0, + "content": "was required; larger values", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 393, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 393, + 505, + 405 + ], + "score": 1.0, + "content": "were unstable and led to premature collapse of training. As shown in Table 1, the scores from", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 404, + 440, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 404, + 440, + 416 + ], + "score": 1.0, + "content": "LOGAN (GD) were worse than LOGAN (NGD) and similar to the baseline model.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 360, + 505, + 416 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 420, + 505, + 520 + ], + "lines": [ + { + "bbox": [ + 105, + 417, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 378, + 447 + ], + "score": 1.0, + "content": "We then evaluate the effects of removing those terms depending on the ordinary gradient (eq. 3). Since these terms were computed", + "type": "text" + }, + { + "bbox": [ + 379, + 420, + 401, + 435 + ], + "score": 0.92, + "content": "\\frac { \\partial f ( z ) } { \\partial z }", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 417, + 505, + 447 + ], + "score": 1.0, + "content": "in eq. 8, which are not inback-propagating through", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 445, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 445, + 505, + 456 + ], + "score": 1.0, + "content": "the latent optimisation procedure, we removed them by selectively blocking back-propagation", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 455, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 106, + 455, + 460, + 468 + ], + "score": 1.0, + "content": "with “stop gradient” operations (e.g., in TensorFlow Abadi et al. 2016). Figure", + "type": "text" + }, + { + "bbox": [ + 460, + 456, + 476, + 466 + ], + "score": 0.69, + "content": "{ \\bf 5 \\ B }", + "type": "inline_equation" + }, + { + "bbox": [ + 477, + 455, + 506, + 468 + ], + "score": 1.0, + "content": "shows", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 466, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 394, + 487 + ], + "score": 1.0, + "content": "the change of FIDs for the three models corresponding to removing", + "type": "text" + }, + { + "bbox": [ + 394, + 466, + 459, + 489 + ], + "score": 0.93, + "content": "\\left( \\frac { \\partial \\Delta z } { \\partial \\theta _ { G } } \\right) ^ { T } \\ \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } }", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 466, + 505, + 487 + ], + "score": 1.0, + "content": ", removing", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 107, + 487, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 107, + 487, + 171, + 510 + ], + "score": 0.92, + "content": "\\begin{array} { r } { \\left( \\frac { \\partial \\Delta z } { \\partial \\theta _ { D } } \\right) ^ { T } \\frac { \\partial f ( z ^ { \\prime } ) } { \\partial z ^ { \\prime } } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 172, + 487, + 505, + 510 + ], + "score": 1.0, + "content": "and removing both terms. As predicted by our analysis (section 3), both terms help", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 507, + 361, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 361, + 520 + ], + "score": 1.0, + "content": "stabilise training; training diverged early for all three ablations.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26.5, + "bbox_fs": [ + 105, + 417, + 506, + 520 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 538, + 252, + 549 + ], + "lines": [ + { + "bbox": [ + 106, + 538, + 254, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 254, + 551 + ], + "score": 1.0, + "content": "5.4 TRUNCATION AND SAMPLES", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 561, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "score": 1.0, + "content": "Truncation is a technique introduced by Brock et al. (2018) to illustrate the trade-off between the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 572, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 350, + 584 + ], + "score": 1.0, + "content": "FID and IS in a trained model. For a model trained with", + "type": "text" + }, + { + "bbox": [ + 351, + 572, + 393, + 583 + ], + "score": 0.91, + "content": "z \\sim p ( z )", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 572, + 505, + 584 + ], + "score": 1.0, + "content": "from a source distribution", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 104, + 582, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 104, + 582, + 355, + 596 + ], + "score": 1.0, + "content": "symmetric around 0, such as the standard normal distribution", + "type": "text" + }, + { + "bbox": [ + 355, + 583, + 388, + 595 + ], + "score": 0.9, + "content": "\\mathcal { N } ( 0 , 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 582, + 506, + 596 + ], + "score": 1.0, + "content": "and the uniform distribution", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 594, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 144, + 606 + ], + "score": 0.91, + "content": "\\mathcal { U } ( - 1 , 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 145, + 594, + 297, + 607 + ], + "score": 1.0, + "content": ", down-scaling (truncating) the source", + "type": "text" + }, + { + "bbox": [ + 297, + 595, + 334, + 604 + ], + "score": 0.9, + "content": "\\bar { z } = s \\cdot z", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 594, + 355, + 607 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 356, + 595, + 398, + 605 + ], + "score": 0.9, + "content": "0 \\leq s \\leq 1", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 594, + 505, + 607 + ], + "score": 1.0, + "content": "gives samples with higher", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "visual quality but reduced diversity. This observation is quantified as higher IS and lower FID when", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 617, + 300, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 300, + 628 + ], + "score": 1.0, + "content": "evaluating samples from truncated distributions.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 33.5, + "bbox_fs": [ + 104, + 561, + 506, + 628 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 632, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 633, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 135, + 645 + ], + "score": 1.0, + "content": "Figure", + "type": "text" + }, + { + "bbox": [ + 136, + 633, + 152, + 643 + ], + "score": 0.6, + "content": "^ { 3 \\mathrm { ~ b ~ } }", + "type": "inline_equation" + }, + { + "bbox": [ + 152, + 633, + 505, + 645 + ], + "score": 1.0, + "content": "plots the truncation curves for the baseline BigGAN-deep model, LOGAN (GD) and", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 644, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 354, + 657 + ], + "score": 1.0, + "content": "LOGAN (NGD), obtained by varying the truncation (value of", + "type": "text" + }, + { + "bbox": [ + 355, + 646, + 361, + 654 + ], + "score": 0.56, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 644, + 506, + 657 + ], + "score": 1.0, + "content": ") from 1.0 (no truncation, upper-left", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "ends of the curves) to 0.02 (extreme truncation, bottom-right ends). Each curve shows the trade-off", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 665, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 506, + 678 + ], + "score": 1.0, + "content": "between FID and IS for an individual model; curves towards the upper-right corner indicate better", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 676, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 505, + 689 + ], + "score": 1.0, + "content": "overall sample quality. The relative positions of curves in Figure 3 (b) shows LOGAN (NGD) has", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "the best sample quality. Interestingly, although LOGAN (GD) and the baseline model have similar", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "score": 1.0, + "content": "scores without truncation (upper-left ends of the curves, see also Table 1), LOGAN (GD) was better", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "behaved with increasing truncation, suggesting LOGAN (GD) still converged to a better equilibrium.", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 720, + 477, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 477, + 733 + ], + "score": 1.0, + "content": "For further reference, we plot truncation curves from additional baseline models in Figure 8.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 41, + "bbox_fs": [ + 105, + 633, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 505, + 160 + ], + "lines": [ + { + "bbox": [ + 106, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "Figure 1 and Figure 2 show samples from chosen points on the truncation curves. In the high IS", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 505, + 106 + ], + "score": 1.0, + "content": "domain, C and D on the truncation curves both have similarly high IS of near 260. Samples from", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "batches with such high IS have almost photo-realistic image quality. Figure 1 show that while", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "the baseline model produced nearly uniform samples, LOGAN (NGD) could still generate highly", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 348, + 140 + ], + "score": 1.0, + "content": "diverse samples. On the other hand, A and B from Figure", + "type": "text" + }, + { + "bbox": [ + 348, + 127, + 364, + 137 + ], + "score": 0.62, + "content": "^ { 3 \\mathrm { ~ b ~ } }", + "type": "inline_equation" + }, + { + "bbox": [ + 364, + 125, + 506, + 140 + ], + "score": 1.0, + "content": "have similarly low FID of near 5,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 313, + 150 + ], + "score": 1.0, + "content": "indicating high sample diversity. Samples in Figure", + "type": "text" + }, + { + "bbox": [ + 313, + 138, + 328, + 148 + ], + "score": 0.49, + "content": "^ { 2 \\mathbf { b } }", + "type": "inline_equation" + }, + { + "bbox": [ + 328, + 137, + 506, + 150 + ], + "score": 1.0, + "content": "show higher quality compared with those in", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 149, + 466, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 466, + 161 + ], + "score": 1.0, + "content": "a (e.g., the interfaces between the elephants and ground, the contours around the pandas).", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3 + }, + { + "type": "title", + "bbox": [ + 107, + 175, + 195, + 188 + ], + "lines": [ + { + "bbox": [ + 105, + 173, + 198, + 191 + ], + "spans": [ + { + "bbox": [ + 105, + 173, + 198, + 191 + ], + "score": 1.0, + "content": "6 CONCLUSION", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 106, + 200, + 505, + 289 + ], + "lines": [ + { + "bbox": [ + 105, + 199, + 505, + 214 + ], + "spans": [ + { + "bbox": [ + 105, + 199, + 505, + 214 + ], + "score": 1.0, + "content": "In this work we present the LOGAN model which significantly improves the state-of-the-art on large", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 211, + 505, + 225 + ], + "spans": [ + { + "bbox": [ + 104, + 211, + 424, + 225 + ], + "score": 1.0, + "content": "scale GAN training for image generation by online optimising the latent source", + "type": "text" + }, + { + "bbox": [ + 425, + 213, + 431, + 221 + ], + "score": 0.61, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 432, + 211, + 505, + 225 + ], + "score": 1.0, + "content": ". Our results illus-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 223, + 504, + 235 + ], + "spans": [ + { + "bbox": [ + 106, + 223, + 504, + 235 + ], + "score": 1.0, + "content": "trate improvements in quantitative evaluation and samples with higher quality and diversity. More-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 233, + 505, + 246 + ], + "spans": [ + { + "bbox": [ + 105, + 233, + 505, + 246 + ], + "score": 1.0, + "content": "over, our analysis suggests that LOGAN fundamentally improves adversarial training dynamics. We", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 244, + 505, + 257 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 505, + 257 + ], + "score": 1.0, + "content": "therefore expect our method to be useful in other tasks that involve adversarial training, including", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 255, + 505, + 268 + ], + "spans": [ + { + "bbox": [ + 104, + 255, + 505, + 268 + ], + "score": 1.0, + "content": "representation learning and inference (Donahue et al., 2017; Dumoulin et al., 2017), text generation", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 266, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 505, + 279 + ], + "score": 1.0, + "content": "(Zhang et al., 2019), style learning (Zhu et al., 2017; Karras et al., 2019), audio generation (Donahue", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 278, + 411, + 290 + ], + "spans": [ + { + "bbox": [ + 106, + 278, + 411, + 290 + ], + "score": 1.0, + "content": "et al., 2018) and video generation (Vondrick et al., 2016; Clark et al., 2019).", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 11.5 + }, + { + "type": "title", + "bbox": [ + 107, + 305, + 175, + 317 + ], + "lines": [ + { + "bbox": [ + 106, + 305, + 176, + 318 + ], + "spans": [ + { + "bbox": [ + 106, + 305, + 176, + 318 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 105, + 322, + 506, + 735 + ], + "lines": [ + { + "bbox": [ + 105, + 323, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 505, + 336 + ], + "score": 1.0, + "content": "Mart´ın Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 115, + 334, + 504, + 348 + ], + "spans": [ + { + "bbox": [ + 115, + 334, + 504, + 348 + ], + "score": 1.0, + "content": "Devin, Sanjay Ghemawat, Geoffrey Irving, Michael Isard, et al. 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In the high IS", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 505, + 106 + ], + "score": 1.0, + "content": "domain, C and D on the truncation curves both have similarly high IS of near 260. Samples from", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "batches with such high IS have almost photo-realistic image quality. Figure 1 show that while", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "the baseline model produced nearly uniform samples, LOGAN (NGD) could still generate highly", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 348, + 140 + ], + "score": 1.0, + "content": "diverse samples. On the other hand, A and B from Figure", + "type": "text" + }, + { + "bbox": [ + 348, + 127, + 364, + 137 + ], + "score": 0.62, + "content": "^ { 3 \\mathrm { ~ b ~ } }", + "type": "inline_equation" + }, + { + "bbox": [ + 364, + 125, + 506, + 140 + ], + "score": 1.0, + "content": "have similarly low FID of near 5,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 313, + 150 + ], + "score": 1.0, + "content": "indicating high sample diversity. 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Figure 8 shows", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 363, + 223, + 376 + ], + "spans": [ + { + "bbox": [ + 106, + 363, + 223, + 376 + ], + "score": 1.0, + "content": "additional truncation curves.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18.5 + }, + { + "type": "title", + "bbox": [ + 107, + 390, + 376, + 404 + ], + "lines": [ + { + "bbox": [ + 105, + 389, + 377, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 377, + 406 + ], + "score": 1.0, + "content": "B DETAILED ANALYSIS OF LATENT OPTIMISATION", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 415, + 505, + 448 + ], + "lines": [ + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "score": 1.0, + "content": "In this section we present three complementary analyses of LOGAN. In particular, we show how the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 426, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 505, + 438 + ], + "score": 1.0, + "content": "algorithm brings together ideas from symplectic gradient adjustment, unrolled GANs and stochastic", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 438, + 253, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 253, + 449 + ], + "score": 1.0, + "content": "approximation with two time scales.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22 + }, + { + "type": "title", + "bbox": [ + 107, + 461, + 363, + 473 + ], + "lines": [ + { + "bbox": [ + 106, + 461, + 365, + 473 + ], + "spans": [ + { + "bbox": [ + 106, + 461, + 365, + 473 + ], + "score": 1.0, + "content": "B.1 APPROXIMATE SYMPLECTIC GRADIENT ADJUSTMENT", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 106, + 481, + 505, + 526 + ], + "lines": [ + { + "bbox": [ + 105, + 480, + 505, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 388, + 495 + ], + "score": 1.0, + "content": "To analyse LOGAN as a differentiable game we treat the latent step", + "type": "text" + }, + { + "bbox": [ + 389, + 482, + 403, + 492 + ], + "score": 0.85, + "content": "\\Delta z", + "type": "inline_equation" + }, + { + "bbox": [ + 404, + 480, + 505, + 495 + ], + "score": 1.0, + "content": "as adding a third player", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 493, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 487, + 505 + ], + "score": 1.0, + "content": "to the original game played by the discriminator and generator. 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Figure 8 shows", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 363, + 223, + 376 + ], + "spans": [ + { + "bbox": [ + 106, + 363, + 223, + 376 + ], + "score": 1.0, + "content": "additional truncation curves.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 352, + 505, + 376 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 390, + 376, + 404 + ], + "lines": [ + { + "bbox": [ + 105, + 389, + 377, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 377, + 406 + ], + "score": 1.0, + "content": "B DETAILED ANALYSIS OF LATENT OPTIMISATION", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 415, + 505, + 448 + ], + "lines": [ + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "score": 1.0, + "content": "In this section we present three complementary analyses of LOGAN. 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This correspondence based on first order", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 322, + 505, + 335 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 505, + 335 + ], + "score": 1.0, + "content": "Taylor expansion is unsurprising, as SGA is based on linearising the adversarial dynamics (Balduzzi", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 333, + 159, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 159, + 346 + ], + "score": 1.0, + "content": "et al., 2018).", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18 + }, + { + "type": "title", + "bbox": [ + 106, + 358, + 373, + 370 + ], + "lines": [ + { + "bbox": [ + 105, + 358, + 374, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 374, + 371 + ], + "score": 1.0, + "content": "B.3 STOCHASTIC APPROXIMATION WITH TWO TIME SCALES", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 106, + 378, + 505, + 468 + ], + "lines": [ + { + "bbox": [ + 105, + 378, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 505, + 392 + ], + "score": 1.0, + "content": "Heusel et al. (2017) used the theory of stochastic approximation to analyse GAN training. View-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 390, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 505, + 403 + ], + "score": 1.0, + "content": "ing the training process as stochastic approximation with two time scales (Borkar, 1997; Konda &", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 401, + 505, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 296, + 414 + ], + "score": 1.0, + "content": "Borkar, 1999), they suggest that the update of", + "type": "text" + }, + { + "bbox": [ + 296, + 402, + 306, + 411 + ], + "score": 0.78, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 401, + 492, + 414 + ], + "score": 1.0, + "content": "should be fast enough compared with that of", + "type": "text" + }, + { + "bbox": [ + 492, + 402, + 501, + 411 + ], + "score": 0.73, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 401, + 505, + 414 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 412, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 412, + 506, + 425 + ], + "score": 1.0, + "content": "Under mild assumptions, Heusel et al. 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Their analysis follows the idea of", + "type": "text" + }, + { + "bbox": [ + 340, + 423, + 362, + 435 + ], + "score": 0.93, + "content": "( \\tau , \\delta )", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 423, + 505, + 435 + ], + "score": 1.0, + "content": "perturbation (Hirsch, 1989), where", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 433, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 176, + 447 + ], + "score": 1.0, + "content": "the slow updates", + "type": "text" + }, + { + "bbox": [ + 176, + 434, + 191, + 445 + ], + "score": 0.75, + "content": "( G )", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 433, + 505, + 447 + ], + "score": 1.0, + "content": "is interpreted as a small perturbation over the ODE describing the fast update", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 107, + 444, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 107, + 445, + 123, + 456 + ], + "score": 0.79, + "content": "( D )", + "type": "inline_equation" + }, + { + "bbox": [ + 123, + 444, + 282, + 459 + ], + "score": 1.0, + "content": ". 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(2017). We start from", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 495, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 203, + 507 + ], + "score": 1.0, + "content": "analysing the change of", + "type": "text" + }, + { + "bbox": [ + 203, + 495, + 216, + 506 + ], + "score": 0.88, + "content": "\\theta _ { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 495, + 369, + 507 + ], + "score": 1.0, + "content": ". 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This correspondence based on first order", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 322, + 505, + 335 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 505, + 335 + ], + "score": 1.0, + "content": "Taylor expansion is unsurprising, as SGA is based on linearising the adversarial dynamics (Balduzzi", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 333, + 159, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 159, + 346 + ], + "score": 1.0, + "content": "et al., 2018).", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 311, + 506, + 346 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 358, + 373, + 370 + ], + "lines": [ + { + "bbox": [ + 105, + 358, + 374, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 374, + 371 + ], + "score": 1.0, + "content": "B.3 STOCHASTIC APPROXIMATION WITH TWO TIME SCALES", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 106, + 378, + 505, + 468 + ], + "lines": [ + { + "bbox": [ + 105, + 378, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 505, + 392 + ], + "score": 1.0, + "content": "Heusel et al. (2017) used the theory of stochastic approximation to analyse GAN training. View-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 390, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 505, + 403 + ], + "score": 1.0, + "content": "ing the training process as stochastic approximation with two time scales (Borkar, 1997; Konda &", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 401, + 505, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 296, + 414 + ], + "score": 1.0, + "content": "Borkar, 1999), they suggest that the update of", + "type": "text" + }, + { + "bbox": [ + 296, + 402, + 306, + 411 + ], + "score": 0.78, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 401, + 492, + 414 + ], + "score": 1.0, + "content": "should be fast enough compared with that of", + "type": "text" + }, + { + "bbox": [ + 492, + 402, + 501, + 411 + ], + "score": 0.73, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 401, + 505, + 414 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 412, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 412, + 506, + 425 + ], + "score": 1.0, + "content": "Under mild assumptions, Heusel et al. (2017) proved that such two time-scale update converges to", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 423, + 505, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 339, + 435 + ], + "score": 1.0, + "content": "local Nash equilibrium. Their analysis follows the idea of", + "type": "text" + }, + { + "bbox": [ + 340, + 423, + 362, + 435 + ], + "score": 0.93, + "content": "( \\tau , \\delta )", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 423, + 505, + 435 + ], + "score": 1.0, + "content": "perturbation (Hirsch, 1989), where", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 433, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 176, + 447 + ], + "score": 1.0, + "content": "the slow updates", + "type": "text" + }, + { + "bbox": [ + 176, + 434, + 191, + 445 + ], + "score": 0.75, + "content": "( G )", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 433, + 505, + 447 + ], + "score": 1.0, + "content": "is interpreted as a small perturbation over the ODE describing the fast update", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 107, + 444, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 107, + 445, + 123, + 456 + ], + "score": 0.79, + "content": "( D )", + "type": "inline_equation" + }, + { + "bbox": [ + 123, + 444, + 282, + 459 + ], + "score": 1.0, + "content": ". Importantly, the size of perturbation", + "type": "text" + }, + { + "bbox": [ + 283, + 446, + 289, + 455 + ], + "score": 0.77, + "content": "\\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 289, + 444, + 505, + 459 + ], + "score": 1.0, + "content": "is measured in the magnitude of parameter change,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 456, + 335, + 469 + ], + "spans": [ + { + "bbox": [ + 106, + 456, + 335, + 469 + ], + "score": 1.0, + "content": "which is affected by both the learning rate and gradients.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 24.5, + "bbox_fs": [ + 105, + 378, + 506, + 469 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 472, + 505, + 518 + ], + "lines": [ + { + "bbox": [ + 105, + 472, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 505, + 485 + ], + "score": 1.0, + "content": "Here we show that LOGAN accelerates discriminator updates and slows down generator updates,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 483, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 505, + 497 + ], + "score": 1.0, + "content": "thus helping the convergence of discriminator according to Heusel et al. 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However, the step of", + "type": "text" + }, + { + "bbox": [ + 230, + 547, + 244, + 558 + ], + "score": 0.86, + "content": "\\Delta z", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 547, + 505, + 560 + ], + "score": 1.0, + "content": "cannot be too large. 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Although this interpretation is not necessary for", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 647, + 494, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 647, + 494, + 661 + ], + "score": 1.0, + "content": "our current algorithm, it may provides useful guidance for incorporating multiple discriminators.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36, + "bbox_fs": [ + 105, + 625, + 505, + 661 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 663, + 505, + 686 + ], + "lines": [ + { + "bbox": [ + 106, + 663, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 663, + 202, + 677 + ], + "score": 1.0, + "content": "We introduce the label", + "type": "text" + }, + { + "bbox": [ + 202, + 665, + 229, + 674 + ], + "score": 0.9, + "content": "t = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 229, + 663, + 302, + 677 + ], + "score": 1.0, + "content": "for real data and", + "type": "text" + }, + { + "bbox": [ + 302, + 665, + 329, + 675 + ], + "score": 0.9, + "content": "t = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 663, + 505, + 677 + ], + "score": 1.0, + "content": "fake samples. This section shows that the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 675, + 189, + 687 + ], + "spans": [ + { + "bbox": [ + 105, + 675, + 189, + 687 + ], + "score": 1.0, + "content": "generator hinge loss", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 663, + 505, + 687 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 268, + 686, + 344, + 699 + ], + "lines": [ + { + "bbox": [ + 268, + 686, + 344, + 699 + ], + "spans": [ + { + "bbox": [ + 268, + 686, + 344, + 699 + ], + "score": 0.93, + "content": "L _ { G } = - D \\left( G ( z ) \\right)", + "type": "interline_equation", + "image_path": "5e64840cde5a5c641e9934aeafb0830a37f1c284d9c281b4f67191fac2af05dc.jpg" + } + ] + } + ], + "index": 40, + "virtual_lines": [ + { + "bbox": [ + 268, + 686, + 344, + 699 + ], + "spans": [], + "index": 40 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 702, + 331, + 714 + ], + "lines": [ + { + "bbox": [ + 105, + 701, + 331, + 716 + ], + "spans": [ + { + "bbox": [ + 105, + 701, + 331, + 716 + ], + "score": 1.0, + "content": "can be interpreted as a negative log-likelihood function:", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41, + "bbox_fs": [ + 105, + 701, + 331, + 716 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 245, + 720, + 366, + 733 + ], + "lines": [ + { + "bbox": [ + 245, + 720, + 366, + 733 + ], + "spans": [ + { + "bbox": [ + 245, + 720, + 366, + 733 + ], + "score": 0.92, + "content": "L _ { G } = - \\ln p ( t = 1 ; D , G ( z ) )", + "type": "interline_equation", + "image_path": "755e51838e95d4086e4f2d4e3f6d5584b88bafa3dac29a07a08babae1248718b.jpg" + } + ] + } + ], + "index": 42, + "virtual_lines": [ + { + "bbox": [ + 245, + 720, + 366, + 733 + ], + "spans": [], + "index": 42 + } + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 105, + 81, + 505, + 105 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 129, + 96 + ], + "score": 1.0, + "content": "Here", + "type": "text" + }, + { + "bbox": [ + 129, + 82, + 201, + 95 + ], + "score": 0.91, + "content": "p ( t = 1 ; z , D , G )", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 81, + 375, + 96 + ], + "score": 1.0, + "content": "is the probability that the generated image", + "type": "text" + }, + { + "bbox": [ + 375, + 83, + 397, + 95 + ], + "score": 0.92, + "content": "G ( z )", + "type": "inline_equation" + }, + { + "bbox": [ + 397, + 81, + 506, + 96 + ], + "score": 1.0, + "content": "can fool the discriminator", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 107, + 92, + 122, + 106 + ], + "spans": [ + { + "bbox": [ + 107, + 94, + 116, + 104 + ], + "score": 0.77, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 116, + 92, + 122, + 106 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 106, + 110, + 506, + 144 + ], + "lines": [ + { + "bbox": [ + 106, + 109, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 106, + 109, + 505, + 123 + ], + "score": 1.0, + "content": "The original GAN’s discriminator can be interpreted as outputting a Bernoulli distribution", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 120, + 506, + 135 + ], + "spans": [ + { + "bbox": [ + 106, + 121, + 232, + 134 + ], + "score": 0.9, + "content": "p ( t ; \\beta _ { G } ) \\mathbf { \\bar { \\alpha } } = \\mathbf { \\alpha } \\beta _ { G } ^ { t } \\cdot ( 1 - \\beta _ { G } ) ^ { 1 - t }", + "type": "inline_equation" + }, + { + "bbox": [ + 233, + 120, + 374, + 135 + ], + "score": 1.0, + "content": ". 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Instead of", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 185, + 505, + 196 + ], + "spans": [ + { + "bbox": [ + 106, + 185, + 173, + 196 + ], + "score": 1.0, + "content": "sampling “1” or", + "type": "text" + }, + { + "bbox": [ + 173, + 185, + 187, + 195 + ], + "score": 0.79, + "content": " { { } ^ { 6 } } { 0 ^ { 9 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 188, + 185, + 505, + 196 + ], + "score": 1.0, + "content": ", we assume that there are many identical discriminators that can independently", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 195, + 505, + 208 + ], + "spans": [ + { + "bbox": [ + 105, + 195, + 343, + 208 + ], + "score": 1.0, + "content": "vote to reject an input sample as fake. The number of votes", + "type": "text" + }, + { + "bbox": [ + 343, + 196, + 350, + 205 + ], + "score": 0.83, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 195, + 505, + 208 + ], + "score": 1.0, + "content": "in a given interval can be described by", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 206, + 367, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 206, + 257, + 218 + ], + "score": 1.0, + "content": "a Poisson distribution with parameter", + "type": "text" + }, + { + "bbox": [ + 258, + 207, + 265, + 216 + ], + "score": 0.81, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 206, + 367, + 218 + ], + "score": 1.0, + "content": "with the following PMF:", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7.5 + }, + { + "type": "interline_equation", + "bbox": [ + 268, + 222, + 342, + 249 + ], + "lines": [ + { + "bbox": [ + 268, + 222, + 342, + 249 + ], + "spans": [ + { + "bbox": [ + 268, + 222, + 342, + 249 + ], + "score": 0.95, + "content": "p ( k ; \\lambda ) = \\frac { \\lambda ^ { k } e ^ { - \\lambda } } { k ! }", + "type": "interline_equation", + "image_path": "573cd2159ad10fe7c4e31950d16db1c118bbf937fdb1deeca3c568b63402b823.jpg" + } + ] + } + ], + "index": 10, + "virtual_lines": [ + { + "bbox": [ + 268, + 222, + 342, + 249 + ], + "spans": [], + "index": 10 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 259, + 505, + 281 + ], + "lines": [ + { + "bbox": [ + 105, + 256, + 504, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 256, + 482, + 273 + ], + "score": 1.0, + "content": "The probability that a generated image can fool all the discriminators is the probability of", + "type": "text" + }, + { + "bbox": [ + 482, + 260, + 504, + 271 + ], + "score": 0.91, + "content": "G ( z )", + "type": "inline_equation" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 270, + 229, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 229, + 282 + ], + "score": 1.0, + "content": "receiving no vote for rejection", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11.5 + }, + { + "type": "interline_equation", + "bbox": [ + 266, + 280, + 344, + 295 + ], + "lines": [ + { + "bbox": [ + 266, + 280, + 344, + 295 + ], + "spans": [ + { + "bbox": [ + 266, + 280, + 344, + 295 + ], + "score": 0.92, + "content": "p ( k = 0 ; \\lambda ) = e ^ { - \\lambda }", + "type": "interline_equation", + "image_path": "a64e4aa0d35d4a74b8b0ce7c8219d18a532639a209e45b708027d63b0f26d3d9.jpg" + } + ] + } + ], + "index": 13, + "virtual_lines": [ + { + "bbox": [ + 266, + 280, + 344, + 295 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 297, + 506, + 320 + ], + "lines": [ + { + "bbox": [ + 106, + 296, + 506, + 311 + ], + "spans": [ + { + "bbox": [ + 106, + 296, + 506, + 311 + ], + "score": 1.0, + "content": "Therefore, we have the following negative log-likelihood as the generator loss if we parameterise", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 306, + 178, + 322 + ], + "spans": [ + { + "bbox": [ + 106, + 308, + 173, + 320 + ], + "score": 0.92, + "content": "\\lambda = - D \\left( G ( z ) \\right)", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 306, + 178, + 322 + ], + "score": 1.0, + "content": ":", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14.5 + }, + { + "type": "interline_equation", + "bbox": [ + 186, + 325, + 425, + 340 + ], + "lines": [ + { + "bbox": [ + 186, + 325, + 425, + 340 + ], + "spans": [ + { + "bbox": [ + 186, + 325, + 425, + 340 + ], + "score": 0.9, + "content": "- \\ln p \\big ( k = 0 ; D , G ( z ) \\big ) = - \\ln p ( k = 0 ; \\lambda ) = - D \\left( G ( z ) \\right)", + "type": "interline_equation", + "image_path": "3d3841bcb9452892eb0bbfa152b70e2643e23e6889ec6905dd315b3e7dd4720c.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 186, + 325, + 425, + 340 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 344, + 504, + 368 + ], + "lines": [ + { + "bbox": [ + 106, + 345, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 106, + 345, + 273, + 358 + ], + "score": 1.0, + "content": "This interpretation has a caveat that when", + "type": "text" + }, + { + "bbox": [ + 273, + 345, + 331, + 357 + ], + "score": 0.93, + "content": "D \\left( G ( z ) \\right) > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 331, + 345, + 505, + 358 + ], + "score": 1.0, + "content": "the Poisson distribution is not well defined.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 355, + 309, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 309, + 369 + ], + "score": 1.0, + "content": "However, in general the discriminator’s hinge loss", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17.5 + }, + { + "type": "interline_equation", + "bbox": [ + 188, + 371, + 423, + 387 + ], + "lines": [ + { + "bbox": [ + 188, + 371, + 423, + 387 + ], + "spans": [ + { + "bbox": [ + 188, + 371, + 423, + 387 + ], + "score": 0.89, + "content": "{ \\cal L } _ { D } = - \\operatorname * { m i n } \\left( 0 , - 1 + D ( x ) \\right) - \\operatorname * { m i n } \\left( 0 , - 1 - D ( G ( z ) ) \\right)", + "type": "interline_equation", + "image_path": "f506e926681df9be3127dca9453aa7f63c40e5f7a47543976a043e5dd36fcbad.jpg" + } + ] + } + ], + "index": 19, + "virtual_lines": [ + { + "bbox": [ + 188, + 371, + 423, + 387 + ], + "spans": [], + "index": 19 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 392, + 245, + 405 + ], + "lines": [ + { + "bbox": [ + 105, + 392, + 246, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 136, + 407 + ], + "score": 1.0, + "content": "pushes", + "type": "text" + }, + { + "bbox": [ + 136, + 392, + 194, + 405 + ], + "score": 0.92, + "content": "D \\left( G ( z ) \\right) < 0", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 392, + 246, + 407 + ], + "score": 1.0, + "content": "via training.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "title", + "bbox": [ + 107, + 419, + 393, + 433 + ], + "lines": [ + { + "bbox": [ + 105, + 419, + 394, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 394, + 435 + ], + "score": 1.0, + "content": "D DETAILS IN COMPUTING DISTANCES IN FIGURE 5 A", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 444, + 505, + 478 + ], + "lines": [ + { + "bbox": [ + 105, + 444, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 206, + 458 + ], + "score": 1.0, + "content": "For a temporal sequence", + "type": "text" + }, + { + "bbox": [ + 206, + 447, + 266, + 457 + ], + "score": 0.9, + "content": "x _ { 1 } , x _ { 2 } , \\ldots , x _ { T }", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 444, + 316, + 458 + ], + "score": 1.0, + "content": "(changes of", + "type": "text" + }, + { + "bbox": [ + 316, + 447, + 322, + 455 + ], + "score": 0.75, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 444, + 334, + 458 + ], + "score": 1.0, + "content": "or", + "type": "text" + }, + { + "bbox": [ + 334, + 445, + 354, + 457 + ], + "score": 0.92, + "content": "f ( z )", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 444, + 505, + 458 + ], + "score": 1.0, + "content": "at each training step in this paper), to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 456, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 106, + 456, + 505, + 468 + ], + "score": 1.0, + "content": "normalise its variance while accounting for the non-stationarity, we process it as follows. We first", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 467, + 421, + 478 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 406, + 478 + ], + "score": 1.0, + "content": "compute the moving average and standard deviation over a window of size", + "type": "text" + }, + { + "bbox": [ + 406, + 467, + 416, + 477 + ], + "score": 0.81, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 468, + 421, + 478 + ], + "score": 1.0, + "content": ":", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23 + }, + { + "type": "interline_equation", + "bbox": [ + 235, + 483, + 376, + 559 + ], + "lines": [ + { + "bbox": [ + 235, + 483, + 376, + 559 + ], + "spans": [ + { + "bbox": [ + 235, + 483, + 376, + 559 + ], + "score": 0.92, + "content": "\\begin{array} { l } { \\displaystyle \\mu _ { t } = \\frac { 1 } { N } \\sum _ { u = t } ^ { t + N - 1 } x _ { u } } \\\\ { \\displaystyle \\sigma _ { t } = \\sqrt { \\frac { 1 } { N - 1 } \\sum _ { u = t } ^ { t + N - 1 } ( x _ { u } - \\mu _ { u } ) ^ { 2 } } } \\end{array}", + "type": "interline_equation", + "image_path": "b0054f0e51f8d020f82fc7d0c8c600504cd099f7774e67ecc59e938693dca699.jpg" + } + ] + } + ], + "index": 25.5, + "virtual_lines": [ + { + "bbox": [ + 235, + 483, + 376, + 521.0 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 235, + 521.0, + 376, + 559.0 + ], + "spans": [], + "index": 26 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 562, + 238, + 574 + ], + "lines": [ + { + "bbox": [ + 106, + 560, + 239, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 560, + 239, + 576 + ], + "score": 1.0, + "content": "Then normalise the sequence as:", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "interline_equation", + "bbox": [ + 287, + 572, + 324, + 595 + ], + "lines": [ + { + "bbox": [ + 287, + 572, + 324, + 595 + ], + "spans": [ + { + "bbox": [ + 287, + 572, + 324, + 595 + ], + "score": 0.91, + "content": "\\bar { x } _ { t } = \\frac { x _ { t } } { \\sigma _ { t } }", + "type": "interline_equation", + "image_path": "e90cbb7d2f2f1acf6e5335ac6e4d56ab6f2452c87406e52e43ed256b920d562c.jpg" + } + ] + } + ], + "index": 28, + "virtual_lines": [ + { + "bbox": [ + 287, + 572, + 324, + 595 + ], + "spans": [], + "index": 28 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 596, + 505, + 619 + ], + "lines": [ + { + "bbox": [ + 106, + 596, + 505, + 609 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 187, + 609 + ], + "score": 1.0, + "content": "The result in Figure", + "type": "text" + }, + { + "bbox": [ + 188, + 597, + 202, + 607 + ], + "score": 0.27, + "content": "{ \\bf 5 a }", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 596, + 448, + 609 + ], + "score": 1.0, + "content": "is robust to the choice of window size. Our experiments with", + "type": "text" + }, + { + "bbox": [ + 449, + 597, + 459, + 606 + ], + "score": 0.8, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 596, + 505, + 609 + ], + "score": 1.0, + "content": "from 10 to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 607, + 239, + 620 + ], + "spans": [ + { + "bbox": [ + 106, + 607, + 239, + 620 + ], + "score": 1.0, + "content": "50 yielded visually similar plots.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29.5 + }, + { + "type": "title", + "bbox": [ + 106, + 634, + 346, + 648 + ], + "lines": [ + { + "bbox": [ + 105, + 635, + 347, + 649 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 347, + 649 + ], + "score": 1.0, + "content": "E EXPERIMENTS WITH DCGAN AND CIFAR", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 659, + 505, + 704 + ], + "lines": [ + { + "bbox": [ + 106, + 660, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 106, + 660, + 505, + 672 + ], + "score": 1.0, + "content": "To test if latent optimisation works with models at more moderate scales, we applied it on SN-GANs", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 671, + 505, + 682 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 505, + 682 + ], + "score": 1.0, + "content": "(Miyato et al., 2018). Although our experiments on this model are less thorough than in the main", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 681, + 505, + 695 + ], + "spans": [ + { + "bbox": [ + 104, + 681, + 505, + 695 + ], + "score": 1.0, + "content": "paper with BigGAN-deep, we hope to provide basic guidelines for researchers interested in applying", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 693, + 261, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 693, + 261, + 705 + ], + "score": 1.0, + "content": "latent optimisation on smaller models.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 33.5 + }, + { + "type": "text", + "bbox": [ + 106, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "The experiments follows the same basic setup and hyper-parameter settings as the CS-GAN in Wu", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 719, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 719, + 505, + 734 + ], + "score": 1.0, + "content": "et al. 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Instead of", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 185, + 505, + 196 + ], + "spans": [ + { + "bbox": [ + 106, + 185, + 173, + 196 + ], + "score": 1.0, + "content": "sampling “1” or", + "type": "text" + }, + { + "bbox": [ + 173, + 185, + 187, + 195 + ], + "score": 0.79, + "content": " { { } ^ { 6 } } { 0 ^ { 9 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 188, + 185, + 505, + 196 + ], + "score": 1.0, + "content": ", we assume that there are many identical discriminators that can independently", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 195, + 505, + 208 + ], + "spans": [ + { + "bbox": [ + 105, + 195, + 343, + 208 + ], + "score": 1.0, + "content": "vote to reject an input sample as fake. The number of votes", + "type": "text" + }, + { + "bbox": [ + 343, + 196, + 350, + 205 + ], + "score": 0.83, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 195, + 505, + 208 + ], + "score": 1.0, + "content": "in a given interval can be described by", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 206, + 367, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 206, + 257, + 218 + ], + "score": 1.0, + "content": "a Poisson distribution with parameter", + "type": "text" + }, + { + "bbox": [ + 258, + 207, + 265, + 216 + ], + "score": 0.81, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 206, + 367, + 218 + ], + "score": 1.0, + "content": "with the following PMF:", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7.5, + "bbox_fs": [ + 105, + 173, + 506, + 218 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 268, + 222, + 342, + 249 + ], + "lines": [ + { + "bbox": [ + 268, + 222, + 342, + 249 + ], + "spans": [ + { + "bbox": [ + 268, + 222, + 342, + 249 + ], + "score": 0.95, + "content": "p ( k ; \\lambda ) = \\frac { \\lambda ^ { k } e ^ { - \\lambda } } { k ! }", + "type": "interline_equation", + "image_path": "573cd2159ad10fe7c4e31950d16db1c118bbf937fdb1deeca3c568b63402b823.jpg" + } + ] + } + ], + "index": 10, + "virtual_lines": [ + { + "bbox": [ + 268, + 222, + 342, + 249 + ], + "spans": [], + "index": 10 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 259, + 505, + 281 + ], + "lines": [ + { + "bbox": [ + 105, + 256, + 504, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 256, + 482, + 273 + ], + "score": 1.0, + "content": "The probability that a generated image can fool all the discriminators is the probability of", + "type": "text" + }, + { + "bbox": [ + 482, + 260, + 504, + 271 + ], + "score": 0.91, + "content": "G ( z )", + "type": "inline_equation" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 270, + 229, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 229, + 282 + ], + "score": 1.0, + "content": "receiving no vote for rejection", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11.5, + "bbox_fs": [ + 105, + 256, + 504, + 282 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 266, + 280, + 344, + 295 + ], + "lines": [ + { + "bbox": [ + 266, + 280, + 344, + 295 + ], + "spans": [ + { + "bbox": [ + 266, + 280, + 344, + 295 + ], + "score": 0.92, + "content": "p ( k = 0 ; 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D , G ( z ) \\big ) = - \\ln p ( k = 0 ; \\lambda ) = - D \\left( G ( z ) \\right)", + "type": "interline_equation", + "image_path": "3d3841bcb9452892eb0bbfa152b70e2643e23e6889ec6905dd315b3e7dd4720c.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 186, + 325, + 425, + 340 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 344, + 504, + 368 + ], + "lines": [ + { + "bbox": [ + 106, + 345, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 106, + 345, + 273, + 358 + ], + "score": 1.0, + "content": "This interpretation has a caveat that when", + "type": "text" + }, + { + "bbox": [ + 273, + 345, + 331, + 357 + ], + "score": 0.93, + "content": "D \\left( G ( z ) \\right) > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 331, + 345, + 505, + 358 + ], + "score": 1.0, + "content": "the Poisson distribution is not well defined.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 355, + 309, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 309, + 369 + ], + "score": 1.0, + "content": "However, in general the discriminator’s hinge loss", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17.5, + "bbox_fs": [ + 105, + 345, + 505, + 369 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 188, + 371, + 423, + 387 + ], + "lines": [ + { + "bbox": [ + 188, + 371, + 423, + 387 + ], + "spans": [ + { + "bbox": [ + 188, + 371, + 423, + 387 + ], + "score": 0.89, + "content": "{ \\cal L } _ { D } = - \\operatorname * { m i n } \\left( 0 , - 1 + D ( x ) \\right) - \\operatorname * { m i n } \\left( 0 , - 1 - D ( G ( z ) ) \\right)", + "type": "interline_equation", + "image_path": "f506e926681df9be3127dca9453aa7f63c40e5f7a47543976a043e5dd36fcbad.jpg" + } + ] + } + ], + "index": 19, + "virtual_lines": [ + { + "bbox": [ + 188, + 371, + 423, + 387 + ], + "spans": [], + "index": 19 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 392, + 245, + 405 + ], + "lines": [ + { + "bbox": [ + 105, + 392, + 246, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 136, + 407 + ], + "score": 1.0, + "content": "pushes", + "type": "text" + }, + { + "bbox": [ + 136, + 392, + 194, + 405 + ], + "score": 0.92, + "content": "D \\left( G ( z ) \\right) < 0", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 392, + 246, + 407 + ], + "score": 1.0, + "content": "via training.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20, + "bbox_fs": [ + 105, + 392, + 246, + 407 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 419, + 393, + 433 + ], + "lines": [ + { + "bbox": [ + 105, + 419, + 394, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 394, + 435 + ], + "score": 1.0, + "content": "D DETAILS IN COMPUTING DISTANCES IN FIGURE 5 A", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 444, + 505, + 478 + ], + "lines": [ + { + "bbox": [ + 105, + 444, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 206, + 458 + ], + "score": 1.0, + "content": "For a temporal sequence", + "type": "text" + }, + { + "bbox": [ + 206, + 447, + 266, + 457 + ], + "score": 0.9, + "content": "x _ { 1 } , x _ { 2 } , \\ldots , x _ { T }", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 444, + 316, + 458 + ], + "score": 1.0, + "content": "(changes of", + "type": "text" + }, + { + "bbox": [ + 316, + 447, + 322, + 455 + ], + "score": 0.75, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 444, + 334, + 458 + ], + "score": 1.0, + "content": "or", + "type": "text" + }, + { + "bbox": [ + 334, + 445, + 354, + 457 + ], + "score": 0.92, + "content": "f ( z )", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 444, + 505, + 458 + ], + "score": 1.0, + "content": "at each training step in this paper), to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 456, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 106, + 456, + 505, + 468 + ], + "score": 1.0, + "content": "normalise its variance while accounting for the non-stationarity, we process it as follows. We first", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 467, + 421, + 478 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 406, + 478 + ], + "score": 1.0, + "content": "compute the moving average and standard deviation over a window of size", + "type": "text" + }, + { + "bbox": [ + 406, + 467, + 416, + 477 + ], + "score": 0.81, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 468, + 421, + 478 + ], + "score": 1.0, + "content": ":", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23, + "bbox_fs": [ + 105, + 444, + 505, + 478 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 235, + 483, + 376, + 559 + ], + "lines": [ + { + "bbox": [ + 235, + 483, + 376, + 559 + ], + "spans": [ + { + "bbox": [ + 235, + 483, + 376, + 559 + ], + "score": 0.92, + "content": "\\begin{array} { l } { \\displaystyle \\mu _ { t } = \\frac { 1 } { N } \\sum _ { u = t } ^ { t + N - 1 } x _ { u } } \\\\ { \\displaystyle \\sigma _ { t } = \\sqrt { \\frac { 1 } { N - 1 } \\sum _ { u = t } ^ { t + N - 1 } ( x _ { u } - \\mu _ { u } ) ^ { 2 } } } \\end{array}", + "type": "interline_equation", + "image_path": "b0054f0e51f8d020f82fc7d0c8c600504cd099f7774e67ecc59e938693dca699.jpg" + } + ] + } + ], + "index": 25.5, + "virtual_lines": [ + { + "bbox": [ + 235, + 483, + 376, + 521.0 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 235, + 521.0, + 376, + 559.0 + ], + "spans": [], + "index": 26 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 562, + 238, + 574 + ], + "lines": [ + { + "bbox": [ + 106, + 560, + 239, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 560, + 239, + 576 + ], + "score": 1.0, + "content": "Then normalise the sequence as:", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27, + "bbox_fs": [ + 106, + 560, + 239, + 576 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 287, + 572, + 324, + 595 + ], + "lines": [ + { + "bbox": [ + 287, + 572, + 324, + 595 + ], + "spans": [ + { + "bbox": [ + 287, + 572, + 324, + 595 + ], + "score": 0.91, + "content": "\\bar { x } _ { t } = \\frac { x _ { t } } { \\sigma _ { t } }", + "type": "interline_equation", + "image_path": "e90cbb7d2f2f1acf6e5335ac6e4d56ab6f2452c87406e52e43ed256b920d562c.jpg" + } + ] + } + ], + "index": 28, + "virtual_lines": [ + { + "bbox": [ + 287, + 572, + 324, + 595 + ], + "spans": [], + "index": 28 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 596, + 505, + 619 + ], + "lines": [ + { + "bbox": [ + 106, + 596, + 505, + 609 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 187, + 609 + ], + "score": 1.0, + "content": "The result in Figure", + "type": "text" + }, + { + "bbox": [ + 188, + 597, + 202, + 607 + ], + "score": 0.27, + "content": "{ \\bf 5 a }", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 596, + 448, + 609 + ], + "score": 1.0, + "content": "is robust to the choice of window size. Our experiments with", + "type": "text" + }, + { + "bbox": [ + 449, + 597, + 459, + 606 + ], + "score": 0.8, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 596, + 505, + 609 + ], + "score": 1.0, + "content": "from 10 to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 607, + 239, + 620 + ], + "spans": [ + { + "bbox": [ + 106, + 607, + 239, + 620 + ], + "score": 1.0, + "content": "50 yielded visually similar plots.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29.5, + "bbox_fs": [ + 106, + 596, + 505, + 620 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 634, + 346, + 648 + ], + "lines": [ + { + "bbox": [ + 105, + 635, + 347, + 649 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 347, + 649 + ], + "score": 1.0, + "content": "E EXPERIMENTS WITH DCGAN AND CIFAR", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 659, + 505, + 704 + ], + "lines": [ + { + "bbox": [ + 106, + 660, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 106, + 660, + 505, + 672 + ], + "score": 1.0, + "content": "To test if latent optimisation works with models at more moderate scales, we applied it on SN-GANs", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 671, + 505, + 682 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 505, + 682 + ], + "score": 1.0, + "content": "(Miyato et al., 2018). Although our experiments on this model are less thorough than in the main", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 681, + 505, + 695 + ], + "spans": [ + { + "bbox": [ + 104, + 681, + 505, + 695 + ], + "score": 1.0, + "content": "paper with BigGAN-deep, we hope to provide basic guidelines for researchers interested in applying", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 693, + 261, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 693, + 261, + 705 + ], + "score": 1.0, + "content": "latent optimisation on smaller models.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 33.5, + "bbox_fs": [ + 104, + 660, + 505, + 705 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "The experiments follows the same basic setup and hyper-parameter settings as the CS-GAN in Wu", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 719, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 719, + 505, + 734 + ], + "score": 1.0, + "content": "et al. 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We reckon that smaller models might not be “over-parametrised”", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 144, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 350, + 156 + ], + "score": 1.0, + "content": "enough to fully amortise the computation from optimising", + "type": "text" + }, + { + "bbox": [ + 350, + 146, + 357, + 153 + ], + "score": 0.65, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 357, + 144, + 505, + 156 + ], + "score": 1.0, + "content": ", which can then further exploit the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 155, + 505, + 166 + ], + "spans": [ + { + "bbox": [ + 106, + 155, + 505, + 166 + ], + "score": 1.0, + "content": "architecture in evaluation time. On the other hand, the overhead from running multiple iterations of", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 165, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 505, + 178 + ], + "score": 1.0, + "content": "latent optimisation is relatively small at this scale. We aim to further investigate this difference in", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 176, + 166, + 188 + ], + "spans": [ + { + "bbox": [ + 106, + 176, + 166, + 188 + ], + "score": 1.0, + "content": "future studies.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 192, + 505, + 238 + ], + "lines": [ + { + "bbox": [ + 105, + 192, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 192, + 505, + 205 + ], + "score": 1.0, + "content": "Table 2 shows the FID and IS alongside SN-GAN and CS-CAN which used the same architec-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 205, + 505, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 505, + 217 + ], + "score": 1.0, + "content": "ture. Here we observe similarly significant improvement over the baseline SN-GAN model, with", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 214, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 185, + 228 + ], + "score": 1.0, + "content": "an improvement of", + "type": "text" + }, + { + "bbox": [ + 185, + 215, + 212, + 226 + ], + "score": 0.88, + "content": "1 6 . 8 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 214, + 252, + 228 + ], + "score": 1.0, + "content": "in IS and", + "type": "text" + }, + { + "bbox": [ + 252, + 215, + 279, + 226 + ], + "score": 0.88, + "content": "3 9 . 6 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 214, + 505, + 228 + ], + "score": 1.0, + "content": "in FID. Figure 9 shows random samples from these two", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 226, + 475, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 475, + 239 + ], + "score": 1.0, + "content": "models. Overall, samples from LOGAN (NGD) have higher contrasts and sharper contours.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10.5 + }, + { + "type": "table", + "bbox": [ + 192, + 294, + 417, + 330 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 256, + 506, + 290 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 257, + 505, + 269 + ], + "spans": [ + { + "bbox": [ + 106, + 257, + 505, + 269 + ], + "score": 1.0, + "content": "Table 2: Comparison of Scores. The first and second columns are reproduced from Miyato et al.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 268, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 106, + 268, + 505, + 280 + ], + "score": 1.0, + "content": "(2018) and Wu et al. (2019) respectively. We report the Inception Score (IS, higher is better, Sali-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 279, + 470, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 279, + 470, + 291 + ], + "score": 1.0, + "content": "mans et al. 2016) and Frechet Inception Distance (FID, lower is better, Heusel et al. 2017). ´", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14 + }, + { + "type": "table_body", + "bbox": [ + 192, + 294, + 417, + 330 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 192, + 294, + 417, + 330 + ], + "spans": [ + { + "bbox": [ + 192, + 294, + 417, + 330 + ], + "score": 0.962, + "html": "
SN-GANCS-GANLOGAN (NGD)
FID29.323.1 ± 0.517.7 ± 0.4
IS7.42 ± 0.087.80 ± 0.058.67 ± 0.05
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We reckon that smaller models might not be “over-parametrised”", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 144, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 350, + 156 + ], + "score": 1.0, + "content": "enough to fully amortise the computation from optimising", + "type": "text" + }, + { + "bbox": [ + 350, + 146, + 357, + 153 + ], + "score": 0.65, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 357, + 144, + 505, + 156 + ], + "score": 1.0, + "content": ", which can then further exploit the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 155, + 505, + 166 + ], + "spans": [ + { + "bbox": [ + 106, + 155, + 505, + 166 + ], + "score": 1.0, + "content": "architecture in evaluation time. On the other hand, the overhead from running multiple iterations of", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 165, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 505, + 178 + ], + "score": 1.0, + "content": "latent optimisation is relatively small at this scale. We aim to further investigate this difference in", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 176, + 166, + 188 + ], + "spans": [ + { + "bbox": [ + 106, + 176, + 166, + 188 + ], + "score": 1.0, + "content": "future studies.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 110, + 505, + 188 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 192, + 505, + 238 + ], + "lines": [ + { + "bbox": [ + 105, + 192, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 192, + 505, + 205 + ], + "score": 1.0, + "content": "Table 2 shows the FID and IS alongside SN-GAN and CS-CAN which used the same architec-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 205, + 505, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 505, + 217 + ], + "score": 1.0, + "content": "ture. Here we observe similarly significant improvement over the baseline SN-GAN model, with", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 214, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 185, + 228 + ], + "score": 1.0, + "content": "an improvement of", + "type": "text" + }, + { + "bbox": [ + 185, + 215, + 212, + 226 + ], + "score": 0.88, + "content": "1 6 . 8 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 214, + 252, + 228 + ], + "score": 1.0, + "content": "in IS and", + "type": "text" + }, + { + "bbox": [ + 252, + 215, + 279, + 226 + ], + "score": 0.88, + "content": "3 9 . 6 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 214, + 505, + 228 + ], + "score": 1.0, + "content": "in FID. Figure 9 shows random samples from these two", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 226, + 475, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 475, + 239 + ], + "score": 1.0, + "content": "models. Overall, samples from LOGAN (NGD) have higher contrasts and sharper contours.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10.5, + "bbox_fs": [ + 105, + 192, + 505, + 239 + ] + }, + { + "type": "table", + "bbox": [ + 192, + 294, + 417, + 330 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 256, + 506, + 290 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 257, + 505, + 269 + ], + "spans": [ + { + "bbox": [ + 106, + 257, + 505, + 269 + ], + "score": 1.0, + "content": "Table 2: Comparison of Scores. The first and second columns are reproduced from Miyato et al.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 268, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 106, + 268, + 505, + 280 + ], + "score": 1.0, + "content": "(2018) and Wu et al. (2019) respectively. We report the Inception Score (IS, higher is better, Sali-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 279, + 470, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 279, + 470, + 291 + ], + "score": 1.0, + "content": "mans et al. 2016) and Frechet Inception Distance (FID, lower is better, Heusel et al. 2017). ´", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14 + }, + { + "type": "table_body", + "bbox": [ + 192, + 294, + 417, + 330 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 192, + 294, + 417, + 330 + ], + "spans": [ + { + "bbox": [ + 192, + 294, + 417, + 330 + ], + "score": 0.962, + "html": "
SN-GANCS-GANLOGAN (NGD)
FID29.323.1 ± 0.517.7 ± 0.4
IS7.42 ± 0.087.80 ± 0.058.67 ± 0.05
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Input: data distribution p(x),latent distribution p(z),D(:; 0D), G(-; 0g),learning rate α, batch size N repeat
Initialise discriminator and generator parameters 0D,0G fori=1 to Ndo
Sample z ~ p(z),x~p(x)
Compute the gradient D(G(z)) and use it to obtain △z from eq. 4 (GD) or eq. 12 (NGD) dz
Optimise the latent z' ← [+ △z],[:] indicates clipping the value between -1 and 1
= -D(G(z))
D(G(z'))-D(x) end for
Compute batch losses LG =N∑i=11 JN (i) and LD=∑=1 N L(i) LD
aLD aLG Update 0D and 0G with the gradients
0D， G
until reaches the maximum training steps
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